Electro-magnetism

West

Reason — When a current passes through a wire from south to north (A to B), it generates a magnetic field around the wire. According to the right-hand rule for electromagnetism, if you wrap your right-hand fingers around the wire in the direction of the current, your thumb will point in the direction of the magnetic field.

So, with the current flowing from A to B, if you curl your fingers around the wire, your thumb would point towards the west. This indicates that the magnetic field is directed towards the west.

concentric circles

Reason — According to the right hand thumb rule, with current passing downward through the cardboard, if we imagine wrapping our right hand around the wire with our fingers pointing downwards, our thumb will point in the direction of the magnetic field lines.

Hence, magnetic field lines would form concentric circles around the wire.

current, magnetic field lines

Reason — According to the right hand thumb rule, the thumb points in the direction of current and fingers encircle the wire in direction of magnetic field lines.

anticlockwise, north pole

Reason — In the figure given above, the direction of current in the loop is anticlockwise. So, it behaves as a north pole .

The strength of magnetic field due to a bar magnet can be changed.

Reason — The strength of magnetic field due to a bar magnet cannot be changed.

The polarity of an electromagnet cannot be changed.

Reason — The polarity of an electromagnet can be reversed by reversing the direction of current in its solenoid.

straight and parallel to the axis of solenoid

Reason — The magnetic field lines inside a solenoid are straight and parallel to the axis of solenoid.

gets reversed in direction

Reason — By reversing the direction of current in a wire, the magnetic field produced by it gets reversed in direction because the polarity of the faces of the wire gets reversed.

all of the above

Reason — Horse shoe magnets are used in :

1. d.c. motor
2. a.c. generator
3. electric bell

Zero

Reason — When two infinitely long parallel wires carry equal currents in the same direction, each wire produces a magnetic field around it according to the right-hand thumb rule.

At the mid-point between the wires, the magnetic field due to one wire is equal in magnitude but opposite in direction to that due to the other wire.

Since these fields act in opposite directions, they cancel each other exactly, resulting in a net magnetic field of zero at the midpoint.

Hence, the magnetic field at the mid-point in between the two wires is zero.

(a) On decreasing current in the wire, the deflection of compass needle decreases which implies that the strength of magnetic field around the wire decreases.

(b) On reversing the direction of current the magnetic needle of compass reverses because the direction of magnetic field reverses.

No, the field line labelled 3 is incorrect and 1, 2 are correct because Magnetic field lines must start from the North pole and end at the South pole outside the magnet but line 3 is shown going from S to N outside the magnet, which is wrong.

As, magnetic field lines go from North to South pole outside a magnet and here the lines are coming out from pole B and entering into pole A.

So, A = South Pole and B = North Pole

(a) Pattern D
Reason — Pattern D shows uniform magnetic field lines because it contains parallel, equally spaced straight lines indicating a uniform magnetic field.

(b) Pattern A
Reason — The pattern for the magnetic field around a straight current carrying wire is concentric circles around it which is shown in pattern A. So, A shows pattern of magnetic field for a straight current carrying wire.

(c) Pattern B
Reason — In pattern B, magnetic field lines are emerging from the loop and curving which is equivalent to a circular current carrying loop. So, B shows pattern depicted by current in a loop.

(a) When a straight wire is lying in a horizontal plane and carrying current from north to south then the direction of magnetic field at a point just underneath is towards east.

(b) The law used is right hand thumb rule.

This face of the coil exhibits North polarity.

(i) The direction of magnetic field at the centre of coil carrying current in clockwise direction is along the axis of coil inwards.

(ii) The direction of magnetic field at the centre of coil carrying current in anticlockwise direction is along the axis of coil outwards.

When a soft iron is introduced inside a solenoid, then the strength of magnetic field increases.

An electric bell is one of the common devices that uses an electromagnet.

(a) When current flows in a wire, it creates magnetic field around it.

(b) On reserving the direction of current in a wire, the magnetic field produced by it gets reversed.

(c) A current carrying solenoid behaves like a bar magnet.

(d) A current carrying solenoid when freely suspended, it always rest in north-south direction.

Right hand thumb rule is used to determine the direction of magnetic field around a current carrying wire.

Right hand thumb rule — If we hold the current carrying conductor in our right hand such that the thumb points in the direction of flow of current, then the fingers encircle the wire in the direction of the magnetic field lines.

In figure, the direction of current in the conductor XY is upwards (i.e., X to Y). The magnetic field lines are anticlockwise around the conductor.

When current flows through the wire, a magnetic field is produced around it. Since the compass needle is placed just below the wire and initially parallel to it, the magnetic field at that point is perpendicular to the wire as given by the right-hand thumb rule.

Due to this magnetic field, the compass needle experiences a torque and deflects from its original position, aligning itself along the direction of the resultant magnetic field.

Polarity at the ends of a current carrying solenoid is determined by the Clock rule.

It states that looking at the face of the loop, if the current in wire around that face is in anticlockwise direction, the face has the north polarity, while if the current at that face is in clockwise direction, the face has the south polarity.

(a) The direction of current in the solenoid at the face A is anticlockwise, so it will have the North polarity and the face B of solenoid at which the current is clockwise will have the South polarity.

(b) The magnet will be repelled because the end A of the solenoid becomes North pole as current at this face is anticlockwise and it repels the north pole of the magnet.

The magnetic field due to a current carrying solenoid can be made stronger —

1. By increasing the number of turns of winding in the solenoid
2. By increasing the current through the solenoid.

x < y

Since, the coil A has less number of turns, therefore the e.m.f. generated in this coil will be less, hence the galvanometer x connected to this coil shows less deflection i.e., x < y.

A current carrying solenoid behaves like a bar magnet so it rests itself in geographic North-South direction.

The needle of the compass will rest in the direction of magnetic field due to solenoid at that point.

(a) When current is passed through the winding of the solenoid, current at end X is in anticlockwise direction so it becomes the North pole. The current at end Y is in clockwise direction so it becomes the South pole.

(b) One way of increasing the strength of electromagnet so formed is by reducing resistance of circuit by means of rheostat to increase current in the coil.

An electromagnet is a temporary strong magnet made by passing current in a coil wound around a piece of soft iron. It is an artificial magnet.

The strength of magnetic field of an electromagnet depends on —

1. Number of turns — By increasing the number of turns of windings in the solenoid, the strength of magnetic field of an electromagnet can be increased.
2. Current — By increasing the current through the solenoid, the strength of magnetic field can be increased.

The strength of an electromagnet can be increased:

1. By increasing the number of turns of winding in the solenoid.
2. By increasing the current through the solenoid.

An electromagnet has the following advantages over an electromagnet —

1. An electromagnet can produce a strong magnetic field.
2. The strength of the magnetic field of an electromagnet can easily be changed by changing the current (or the number of turns) in the solenoid.

Comparison of an electromagnet with a permanent magnet

The soft iron bar is used as the core of the electromagnet in an electric bell because it has low retentivity and therefore, the bar remains magnetized so long the electric current flows through the solenoid, but it gets demagnetized as soon as the current is switched off.

If an a.c. source is used in place of battery, the core of electromagnet will get magnetized, but the polarity at it's ends will change. Since attraction of armature does not depend on the polarity of electromagnet, so the bell will still ring on pressing the switch.

The material used for making the armature of an electric bell is soft iron.

It is used as the core of the electromagnet in an electric bell because it has low retentivity and therefore, the bar remains magnetized so long as the electric current flows through the solenoid but it gets demagnetized as soon as the current is switched off.

Experiment:

In figure below, AB is a wire lying in the north-south direction and connected to a battery through a rheostat and a tapping key. A compass needle is placed just below the wire.

Observation —

(1) When the key is open i.e., no current passes through the wire, the needle points in the N-S direction (i.e., along the earth's magnetic field) with the north pole of needle pointing towards the north direction. In this position, the needle is parallel to the wire as shown in Fig. (a).

(2) When the key is pressed, a current passes in the wire in the direction from A to B (i.e. from south to north) and the north pole (N) of the needle deflects towards the west [Fig.(b)].

(3) When the direction of current in the wire is reversed by reversing the connections at the terminals of the battery, north pole (N) of the needle deflects towards the east [Fig.(c)].

(4) If the compass needle is placed just above the wire, the north pole (N) deflects towards east when the direction of current in wire is from A to B [Fig. (d)], but the needle deflects towards west as in figure (e), if the direction of current in wire is from B to A.

Through the experiment we can say that, when electric current is passed through a conducting wire, a magnetic field is produced around it.

Below diagram shows the direction of three magnetic field lines due to a straight wire carrying current:

The current in the wire is in clockwise direction.

Below diagram shows the magnetic field lines of a loop carrying current:

Below diagrams shows the magnetic field lines along the axis of a current carrying solenoid with the direction of current and direction of magnetic field lines marked:

(a) With the help of the Right hand thumb rule, we get the polarity at A — North pole and at B — South pole.

(b) The end A of the coil behaves like north pole and repels north pole of compass needle. Hence, the compass needle deflects towards west.

Below circuit diagram shows an electromagnet made from a soft iron bar by using a cell, an insulated coil of copper and a switch with its poles labelled:

(a) Solenoid is a cylindrical coil of diameter less than its length.

(b) The device so obtained is an electromagnet.

(c) It is used in an electric relay.

Below circuit diagram shows an electromagnet made by winding a wire on a U-shaped piece of soft iron:

(a) When current is passed through the windings, the end A of the arm becomes south pole (current at this face is clockwise) and the end B becomes north pole (current at this face is in anticlockwise direction).

(b) When the direction of current is reversed then the polarity will also reverse. A will become north pole (current at this face is in anticlockwise direction) and B will become south pole (current at this face is clockwise).

(c) The strength of magnetic field produced can be increased by increasing the current.

The completed diagram of the electric bell with winding of coil drawn is shown below:

Lorentz force

Reason — Lorentz, found that a charge moving in a magnetic field in a direction other than the direction of the magnetic field experiences a force called Lorentz force.

all of the above

Reason — The magnitude of force acting on a current carrying wire placed in a magnetic field in a direction perpendicular to its length depends on :

1. The current flowing in the wire
2. The strength of the magnetic field
3. The length of the wire.

increasing the area of the coil

Reason — One way to increase the speed of rotation of coil, is by increasing the area of the coil. When the area of the coil is increased, more magnetic field lines are intersected as the coil rotates, leading to a greater change in magnetic flux and hence a higher induced EMF and higher speed of rotation.

reverse the direction of the current

Reason — The function of a split ring commutator is to reverse the direction of the current.

torque on loop S is maximum.

Reason — When a current-carrying loop is placed in a uniform magnetic field, the torque acting on it depends upon :

• Strength of the magnetic field
• Area of the loop
• Magnitude of current flowing
• Orientation of the loop relative to the magnetic field

Here, all four loops are placed with same orientation with same current and magnetic field so now the torque is directly proportional to the area (A) enclosed by the loop.

All four loops are made from wires of the same length (2 m), but different shapes enclose different areas. For a given perimeter, a circular loop encloses the maximum area.

Since loop S is circular, it has the largest area among P, Q, R, and S, and therefore experiences the maximum torque.

When the current is reversed in the conductor placed in a magnetic field, the direction of force is also reversed.

During the working of a d.c. motor electrical energy converts into mechanical energy.

The force will act towards West.

Reason — From Fleming's left hand rule, as central finger points towards north (current direction) and forefinger points downwards (magnetic field direction) then thumb will point towards west (force direction).

The force will act towards North.

Reason — Here direction of current will be same as direction of motion of proton. From Fleming's left hand rule when the central finger points towards east (direction of proton) and forefinger points (downward) then direction of magnetic force will be given by thumb which is pointing in the north direction.

Experimentally, it is found that the magnitude of force acting on a current carrying conductor placed in a magnetic field in the direction perpendicular to it's length, depends on the following three factors —

1. The force F is directly proportional to the strength of magnetic field B, i.e., F α B
2. The force F is directly proportional to the current I flowing in the wire, i.e., F α I
3. The force F is directly proportional to the length L of the wire (within the magnetic field) i.e., F α L

(a) The magnitude of force on a current carrying conductor placed in a magnetic field is zero, when current in conductor is in the direction of magnetic field.

(b) The magnitude of force on a current carrying conductor placed in a magnetic field is maximum, when current in conductor is normal to the magnetic field.

The direction of force on a current carrying conductor placed in a magnetic field is obtained by the Fleming's left hand rule.

Fleming's left hand rule — Stretch the forefinger, central finger and the thumb of your left hand mutually perpendicular to each other as shown in figure. If the forefinger indicates the direction of magnetic field and the central finger indicates the direction of current, then the thumb will indicate the direction of motion of conductor.

Fleming's left hand rule — Stretch the forefinger, central finger and the thumb of your left hand mutually perpendicular to each other as shown in figure. If the forefinger indicates the direction of magnetic field and the central finger indicates the direction of current, then the thumb will indicate the direction of motion of conductor.

An electric motor is a device which converts the electrical energy into the mechanical energy.

Principle — An electric motor (dc motor) works on the principle that on passing electric current through a conductor placed normally in a magnetic field, a force acts on the conductor as a result of which the conductor begins to move and thus mechanical energy (or work) is obtained.

The speed of rotation of an electric motor can be increased —

1. By increasing the strength of current in the coil.
2. By increasing the number of turns in the coil.

Electric motors are used in electrical gadgets like fan, washing machine, etc.

According to Fleming’s Left Hand Rule, the direction of force on a current-carrying conductor placed in a magnetic field depends on:

• Forefinger → Direction of magnetic field (from North to South)
• Middle finger → Direction of current
• Thumb → Direction of the force (motion) on the wire

In this case:

• The current in the wire can flow in 2 directions (forward or reversed using the switch).
• The magnetic field can also be in 2 directions (from North to South or South to North, depending on polarity).

So, the force on the wire can act in:

2 (current directions) x 2 (field directions) = 4 different directions

Thus, the force on the wire can act in 4 possible directions.

• Particle A is negatively charged.
• Particle B is uncharged (neutral).
• Particle C is positively charged.

Rule used: Fleming's left-hand rule

Explanation:

According to Fleming's left-hand rule:

• Forefinger shows the direction of magnetic field,
• Middle finger shows the direction of current,
• Thumb shows the direction of force.

Here, the magnetic field is out of the plane of the paper and the particles move towards the right.

For a positive charge, the current is taken in the direction of motion. So, on applying Fleming's left-hand rule, the force acts downwards.

Therefore:

• C, which deflects downwards, is positively charged.
• A, which deflects upwards, is negatively charged, since a negative charge is deflected opposite to a positive charge.
• B remains undeflected, so it is uncharged.

(a) When a current is passed in the coil, the coil experiences a torque due to which it rotates.

(b) The coil will come to rest when it's plane becomes normal to the magnetic field.

(c) Maximum — The couple acting on the coil be maximum, when the plane of coil is parallel to the magnetic field.
Minimum — The couple acting on the coil be minimum, when the plane of coil is normal to the magnetic field.

(d) The instrument which makes use of the principle is D.C. Motor.

(a) The coil begins to rotate in anticlockwise direction, when current is passed through the coil in direction ABCD by connecting a battery between the ends A and D of the coil.

(b) A commutator is necessary for the continuous rotation of coil because the arms AB and CD get interchanged after half rotation, so the direction of torque on coil reverses. To keep the coil rotating in the same direction, a commutator is needed to reverse the direction of current in the coil after each half rotation of coil.

(c) Completed diagram with commutator showing the flow of current in the coil is given below:

Below diagram shows a d.c motor with its parts labelled:

Mechanical to electrical

Reason — In electromagnetic induction, energy transformation occurs due to the relative motion between a magnetic field and a conductor, which induces an electromotive force (EMF) in the conductor. This induced EMF can then drive an electric current through the conductor, thereby converting mechanical energy into electrical energy.

Both the number of turns in the coil and the rate of change of magnetic flux through it

Reason — The magnitude of induced emf depends on the :

1. number of turns in the coil
2. rate of change of magnetic flux linked with each turn

conservation of energy

Reason — Lenz's law is based on the law of conservation of energy. It shows that the mechanical energy is spent in doing work against the opposing force experienced by the moving magnet, and it is transformed into the electrical energy due to which current flows in the solenoid.

e = e_o sin 2πnt

Reason — In an a.c. generator the coil makes n rotations per second. The magnitude of induced emf at any instant is given by e = e_o sin 2πnt.

d.c., a.c.

Reason — A current of constant magnitude and unique direction is called direct current (d.c.).

A current changing its magnitude and direction periodically is called alternating current (a.c.).

Fleming's right hand rule

Reason — The direction of induced current is obtained by Fleming's right hand rule.

Fleming's right hand rule — Stretch the thumb, central finger and forefinger of your right hand mutually perpendicular to each other. If the forefinger indicates the direction of magnetic field and the thumb indicates the direction of motion of the conductor, then the central finger will indicate the direction of induced current.

N_s > N_p

Reason — In a step up transformer the number of turns in the secondary coil is more than the number of turns in the primary coil (N_s > N_p) i.e., turns ratio n > 1. which increases the a.c. voltage and decreases the current. i.e., E_s > E_p and I_s < I_p.

decreases, increases

Reason — In a step up transformer the number of turns in the secondary coil is more than the number of turns in the primary coil ( N_s > N_p) i.e., turns ratio n > 1 which increases the a.c. voltage and decreases the current. i.e., E_s > E_p and I_s < I_p.

In a step down transformer the number of turns in the secondary coil is less than the number of turns in the primary coil (N_s < N_p) i.e., turns ratio n < 1 which decreases the a.c. voltage and increases the current. i.e., E_s < E_p and I_s > I_p.

A transformer can be used with d.c.

Reason — Transformers are used with a.c. circuits to step up or step down voltage. In d.c. circuits, since the current is constant, induction cannot happen. Therefore, transformers are not used with d.c. circuits.

(ii) only

Reason — Induced emf is produced only when there is a change in magnetic flux through the coil.

When the magnet is rotated about its own axis (i), the magnetic field linked with the coil does not change, so no emf is induced.

However, when it is rotated about an axis perpendicular to its length (ii), the magnetic flux through the coil changes continuously, thus inducing an emf.

Hence, the induced emf is generated at the terminals of the coil in (ii) only

(i) 100 W

(ii) 200 V

Reason —

(i) In an ideal transformer (no energy loss), the input power equals output power. Therefore, even though the number of turns changes, the power remains the same.

Hence, the secondary coil also delivers 100 W.

(ii) Given,

• Ratio of number of turns in the secondary coil to the primary coil = 20
• Voltage of the primary coil = 10 V

In a transformer, voltage is proportional to the number of turns i.e.,

$$\begin{aligned}\frac{\text {Voltage of the primary coil}}{\text {Voltage of the secondary coil}} = \frac{\text {Number of turns in the secondary coil}}{\text {Number of turns in the primary coil}} \\[1em] \Rightarrow \text {Voltage of the secondary coil} = \frac{\text {Number of turns in the primary coil}}{\text {Number of turns in the secondary coil}} \times \text {Voltage of the primary coil} \\[1em] = 20 \times 10 \\[1em] = 200\ \text V\end{aligned}$$

Hence, the voltage of the secondary coil is 200 V.

adcb

Reason — As the electron moves away, the magnetic flux through the coil decreases. By Lenz’s law, the induced current flows so as to oppose this decrease. That requires the coil to produce magnetic field into the plane of the paper, which is produced by a clockwise current. In the given diagram, clockwise is adcb.

Hence, the direction of induced current in the coil will be adcb.

anticlockwise

Reason — As the north pole of the magnet is brought closer to the metallic ring, the magnetic flux through the ring increases.

According to Lenz’s law, the induced current flows in such a direction as to oppose this increase in flux so to oppose the approaching north pole, the face of the ring towards the magnet must behave like a north pole.

For a circular loop, this happens when the current flows anticlockwise (as seen from the magnet side).

Hence, the direction of induced current will be anticlockwise.

AB

Reason — The magnetic field around a straight current-carrying conductor is given by the right-hand thumb rule.

• For the wire along OX, at points above the X-axis, the magnetic field is out of the plane of the paper.
• For the wire along OY, at points to the right of the Y-axis, the magnetic field is into the plane of the paper.

Thus, on line AB, the magnetic fields due to the two wires are in opposite directions.

Also, every point on line AB is equidistant from the X-axis and Y-axis, so the magnitudes of the two magnetic fields are equal, since both wires carry the same current.

Therefore, the two magnetic fields cancel each other on AB.

Hence, the magnetic field is zero on line AB.

both A and R are true and R is not the correct explanation of A.

Explanation

Assertion (A) is true. A current-carrying solenoid behaves like a magnet and aligns itself in the north-south direction when freely suspended, similar to a bar magnet. This behavior is due to the magnetic field produced by the current flowing through the solenoid.

Reason (R) is true. The direction of the magnetic field inside a solenoid depends on the direction of the current. The end of the solenoid where the current circulates anti-clockwise acts as a north pole, while the end where the current circulates clockwise acts as a south pole.

But here reason does not justify its assertion.

assertion is true but reason is false.

Explanation

Assertion (A) is true. The strength of the magnetic field produced due to a current carrying circular coil increases with an increase in the strength of the current. This is consistent with Ampere's law, which states that the magnetic field is directly proportional to the current flowing through the coil.

Reason (R) is false. The magnetic field strength is directly proportional to the current flowing through a coil, not inversely proportional.

assertion is true but reason is false.

Explanation

Assertion (A) is true. A transformer can increase the voltage of an alternating electromotive force (e.m.f.). This is accomplished through electromagnetic induction, where a changing magnetic field in the primary coil induces a voltage in the secondary coil.

Reason (R) is false. To increase the voltage in the secondary coil, the number of turns in the secondary coil must be greater than the number of turns in the primary coil, not less. This allows for a step-up transformation of voltage.

both A and R are true R is not the correct explanation of A.

Explanation

Assertion (A) is true. A transformer cannot be used with direct current (DC) because it relies on the principle of electromagnetic induction, which requires a changing magnetic field. In DC, the current flows in one direction without changing, so there is no alternating magnetic field to induce voltage in the secondary coil of the transformer.

Reason (R) is true. The lamination of the core in a transformer is used to prevent energy loss due to induced currents in the core, known as eddy currents. By laminating the core, the magnetic flux is confined to the individual lamination, reducing the eddy current losses

both A and R are true and R is the correct explanation of A.

Explanation

Assertion (A) is true. According to Faraday's law of electromagnetic induction, the magnitude of the induced electromotive force (e.m.f.) in a coil is maximum when the rate of change of magnetic flux through the coil is maximum. This occurs when the magnetic flux linked with the coil reduces to zero from its maximum value, resulting in the maximum rate of change of magnetic flux.

Reason (R) is true. This happens when the plane of the coil lies in the direction of the magnetic field. When the coil is in this position, the magnetic flux through the coil is changing most rapidly, resulting in the maximum induced e.m.f.

(a) When a magnet is moved towards a coil having a galvanometer between it's ends then mechanical energy changes to the electrical energy.

(b) The phenomenon is known as Electromagnetic Induction.

The current is induced in a closed circuit only if there is change in number of magnetic field lines linked with the circuit.

(i) Yes, e.m.f. is induced because when current is started in a wire held near a loop of wire, magnetic field varies due to which e.m.f. is induced.

(ii) Yes, e.m.f. is induced because when current is switched off in a wire held near a loop of wire, the current stops and magnetic field again varies and hence e.m.f. is induced.

(iii) Yes, e.m.f. is induced. When there is a relative motion between the magnet and a loop of wire, magnetic flux changes and e.m.f. is induced.

(iv) No, e.m.f. is not induced. When a loop of wire is held near a magnet, there is no change in magnetic field hence e.m.f. is not induced.

The frequency of rotations of the coil (i.e., the number of rotations of the coil per second) determines the frequency of a.c. produced in a generator.

An a.c. generator changes the mechanical energy to electrical energy.

The mechanical energy changes into the electrical energy in a generator when it is in use.

The advantage of a.c. over d.c. is that it is cheaper and easy to generate a.c. than d.c.

E.m.f. in the primary and secondary coils of a transformer are related with the number of turns in these coils as follows —

$\frac{\text E_\text s}{\text E_\text p}$ = $\frac{\text N_\text s}{\text N_\text p}$

where s stands for secondary, p stands for primary, E is E.m.f and N is number of turns in the coils .

(i) In a step up transformer, the number of turns in the primary are less than the number of turns in the secondary.

(ii) The transformer is used in alternating current circuits.

(iii) In a transformer, the frequency of a.c. voltage remains same.

The material used in —

(a) an electric bell — soft iron core

(b) electromagnet — soft iron core

(c) a d.c. motor — soft iron core

(d) an a.c. generator — soft iron core

(e) a transformer — soft iron core

Faraday formulated the following two laws of electromagnetic induction —

1. Whenever there is a change in magnetic flux linked with a coil, an e.m.f. is induced. The e.m.f. induced lasts so long there is a change in the magnetic flux linked with the coil.
2. The magnitude of e.m.f. induced is directly proportional to the rate of change of magnetic flux linked with the coil. If magnetic flux changes at a constant rate, a steady e.m.f. is produced.

The magnitude of induced e.m.f. in a coil depend on following two factors —

1. The rate of change in magnetic flux with each turn of coil, and
2. The number of turns in the coil.

(a) When there is a relative motion between the coil and magnet, magnetic flux linked with the coil changes. As shown in figure b, the coil is moved towards the north pole of magnet, so the magnetic flux through the coil increases. Similarly, if the coil is moved away from the north pole of magnet, the magnetic flux through the coil decreases.
Due to change in the magnetic flux linked with the coil, an e.m.f. is induced in the coil. The induced e.m.f. causes a current to flow in the coil if the circuit of coil is closed.

(b) the source of energy associated with the current obtained in part (a) is the Mechanical energy spent in moving the magnet relative to the coil.

Fleming's right hand rule — Stretch the thumb, central finger and forefinger of your right hand mutually perpendicular to each other. If the forefinger indicates the direction of magnetic field and the thumb indicates the direction of motion of the conductor, then the central finger will indicate the direction of induced current.

According to Lenz's law, the direction of induced e.m.f. (or induced current) is such that it opposes the cause which produces it.

According to Lenz's law, the direction of induced e.m.f. (or induced current) is such that it opposes the cause which produces it. As per Faraday's laws of Electromagnetic Induction, the magnitude of induced e.m.f. is directly proportional to the number of turns in the coil.
Hence, the e.m.f. induced in the coil becomes more when the number of turns in the coil are increased. As a result, a stronger magnetic field is induced that opposes the motion of magnet towards the coil with a greater force making it more difficult to move the magnet towards the coil.

Due to law of conservation of energy, the mechanical energy spent in producing the change is transformed into the electrical energy in form of the induced current. Hence, the induced current flows in a direction to oppose the change so that some mechanical energy is constantly required to overcome the opposing force which in turn will keep the induced current flowing.

An A.C. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.

Principle — In a generator, a coil is rotated in a magnetic field. Due to rotation, the magnetic flux linked with the coil changes and therefore an e.m.f. is induced between the ends of the coil. Thus, a generator acts as a source of current in an external circuit containing load when connected between the ends of it's coil.

Use — We use a.c. generator in our house as an alternative source of electricity when electric supply from mains is not available.

(a) When in an a.c generator the speed at which the coil rotates is doubled the frequency of output voltage is also doubled.

(b) The maximum output voltage is also doubled when the speed at which the coil rotates is doubled.

Two ways to produce a higher e.m.f. in an a.c. generator are —

1. By increasing the speed of rotation of coil.
2. By increasing the number of turns in the coil.

(i) Dis-similarities between a d.c. motor and an a.c. generator are —

(ii) Similarities between a d.c. motor and an a.c. generator are —

(i) Both in d.c. motor and an a.c. generator, a coil rotates in a magnetic field between the pole pieces of a powerful electromagnet.

(ii) Both in a d.c. motor and an a.c. generator, there is a transformation of energy from one form to the other form.

Transformers are used to step up or step down the a.c. voltage. They work on a.c. current.

Factors on which the magnitude of an induced e.m.f. in the secondary coil of a transformer depends are —

1. The turns ratio i.e., the number of turns in the secondary coil to the number of turns in the primary coil.
2. The input voltage.

The device used to transform 12 V a.c. to 200 V a.c. is step up transformer. It works on the principle of electromagnetic induction.

(i) Step up transformer — The wire in the primary coil is thicker than that in the secondary coil. It is done because the current in the primary coil is more than in the secondary coil and a thick wire results in less resistance and therefore less loss of energy as heat.

(ii) Step down transformer — The wire in the secondary coil is thicker than that in the primary coil. It is done so because the current in the secondary coil is more than in the primary coil and a thick wire results in less resistance and therefore less loss of energy as heat.

For an ideal transformer, input power is equal to the output power. From relation P = VI, (where P is power, V is voltage and I is current) , we know that V and I are inversely related. In a step down transformer voltage is decreased and in order to keep the power same the output current increases.

The laminated core prevents the loss of energy due to induced (or eddy) currents in the core. Hence, it is made laminated (thin sheets) instead of being in one solid piece.

The two kinds of energy losses are —

1. Loss of energy due to induced (or eddy) currents. The use of laminated core prevents this loss of energy.
2. Hysteresis loss — The use of soft iron for the core helps in minimization of this loss.

Difference between a step up transformer and step down transformer are:

The transformer used in the —

(i) Power generating station — Step up transformer is used in Power generating station to increase the alternating voltage from 11 kV to 132 kV.

(ii) Power sub station — Step down transformer is used in Power sub station to decrease the alternating voltage from 132 kV to 33 kV and then further to 11 kV and to 220 V.

(a) Whenever there is a change in the number of magnetic field lines linked with a conductor, an electromotive force (e.m.f.) is developed between the ends of the conductor which lasts as long as there is a change in the number of magnetic field lines through the conductor. This phenomenon is called the electromagnetic induction.

(b) Demonstration of the phenomenon of electromagnetic induction —

Experiment — Wind an insulated copper wire in form of a spiral on a paper (or wooden) cylinder so as to form a coil in the form of a solenoid. Connect a centre zero galvanometer G between the two ends of the solenoid. Then, place a magnet NS at some distance along the axis of solenoids as shown in figure.

Observations — It is observed that,

(i) When the magnet is stationary, there is no deflection in galvanometer and it's pointer reads zero as shown in figure (a).

(ii) When the magnet with it's north pole facing the solenoid is moved towards it, the galvanometer shows a deflection towards right showing that a current flows in solenoid in the direction B to A as shown in figure (b).

(iii) As the motion of magnet is stopped, the pointer of galvanometer comes to zero position. Fig. (c) This shows that the current in solenoid flows as long as the magnet is in motion.

(iv) If the magnet is moved away from the solenoid, the pointer of galvanometer deflects towards left (as shown in figure d) showing that the current in solenoid flows again, but now in direction A to B which is opposite to that as shown in figure b. Current becomes zero as soon as the magnet stops.

(v) If the same action (movement) of magnet is done rapidly, the deflection in the galvanometer is more than before although the direction of deflection remains same. It shows that now more current flows.

(vi) If the magnet is brought towards the solenoid by keeping it's south pole towards it, the pointer of galvanometer deflects towards left as shown in figure (e) showing that the current in solenoid flows in direction A to B which is opposite to that shown in figure (b)

(a) When there is a relative motion between the coil and magnet, magnetic flux linked with the coil changes. As shown in figure b, the coil is moved towards the north pole of magnet, so the magnetic flux through the coil increases. Similarly, if the coil is moved away from the north pole of magnet, the magnetic flux through the coil decreases. Due to change in the magnetic flux linked with the coil, an e.m.f. is induced in the coil. The induced e.m.f. causes a current to flow in the coil if the circuit of coil is closed.

(b) The magnitude of induced e.m.f. depends on the rate of change of magnetic flux linked with each turn.

(c) The direction of induced e.m.f. depends on whether there is an increase or decrease in the magnetic flux. It can be determined by any of the following two rules (i) Fleming's right hand rule, (ii) Lenz's law.

Lenz's law is based on the law of conservation of energy. It shows that the mechanical energy is spent in doing work against the opposing force experienced by the moving magnet, and it is transformed into the electrical energy due to which current flows in the solenoid.

(i) When north pole of the magnet is brought towards the end B of the solenoid, the induced current flows in the solenoid in direction A to B i.e., at the end B, the current is anticlockwise, so the end B of the solenoid becomes a north pole to repel the magnet. Thus it opposes the motion of north pole of the magnet towards the solenoid, which is the cause producing it.

(ii) The law used to arrive at the conclusion in part (i) is Lenz's law.

(iii) (a) Current is directly proportional to the number of turns. Hence, current becomes twice when the coil has twice the number of turns.

(b) The current in coil becomes thrice when the coil was made to move three times fast .

(a) (i) A deflection is observed in the galvanometer towards the right when the magnet is moved away rapidly.

(ii) The deflection becomes zero, when the magnet is kept stationary after it has moved into the coil.

(iii) The deflection again occurs in opposite direction, when the magnet is rapidly pulled out of the coil.

(b) When a more powerful magnet is used then the deflection is increased.

Labelled diagram of a simple a.c generator is given below:

Below diagrams shows the various components of a step up transformer:

Labelled diagram of a step up transformer is given below:

The transformer used to change a low alternating voltage to a high alternating voltage (of same frequency) is called a step up transformer (i.e. E_s > E_p).

When the terminals of primary coil are connected to the source of alternating e.m.f. a varying current flows through the primary coil. This varying current produces a varying magnetic field in the core of the transformer.Thus the magnetic flux linked with the secondary coil vary due to which an e.m.f. is induced in it. The induced e.m.f. varies in the same manner as the applied e.m.f. in the primary coil varies and thus the induced e.m.f. has the same frequency as that of the applied e.m.f.

In a step up transformer the number of turns in the secondary coil is more than the number of turns in the primary coil ( N_s > N_p) i.e., turns ratio n > 1 as shown above.

Since current in primary coil is more than in the secondary coil (or I_p > I_s), so the wire in the primary coil is kept thicker than in the secondary coil.

Two characteristics of the primary coil as compared to it's secondary coil are —

1. The number of turns in the primary coil are less than that of the secondary coil.
2. The wire of the primary coil is thicker than that of the secondary coil.

The labelled diagram of a device used to transform 220 V a.c. to 15 V a.c. is given below:

Name of this device is Step Down Transformer. It is used to change a high alternating voltage to a low alternating voltage (of same frequency).

When the terminals of primary coil are connected to the source of alternating e.m.f. a varying current flows through the primary coil. This varying current produces a varying magnetic field in the core of the transformer. Thus the magnetic flux linked with the secondary coil vary due to which an e.m.f. is induced in it. The induced e.m.f. varies in the same manner as the applied e.m.f. in the primary coil varies and thus the induced e.m.f. has the same frequency as that of the applied e.m.f.

In a step down transformer the number of turns in the secondary coil are less than the number of turns in the primary coil (N_s < N_p) i.e., turns ratio n < 1 as shown in figure. Since current in secondary coil is more than in the primary coil (i.e., I_s > I_p ) so the wire in secondary coil is kept thicker than in the primary coil.

Uses of a step down transformer —

1. With electric bells, night electric bulbs, mobile phones, computers etc.
2. At the power sub-stations to step down the voltage before it's distribution to the consumers.

(a) Completed and labelled diagram is shown below:

(b) The part drawn is the core.

(c) It is a soft iron core.

(d) This is a step down transformer because the number of turns in the secondary coil are less than the primary coil.

(a) The material used for the core is soft iron. It is made up from thin laminated sheets of soft iron of T and U shape, placed alternately one above the other and insulated from each other by paint (or varnish) coating over them.

(b) Completed diagram is shown below:

(c) As 220 V is converted to 44 V hence, it is a step down transformer.

(a) North pole of needle deflects towards east.

(b) On passing current through the wire AB, a magnetic field is produced around the wire which aligns the magnetic needle in it's direction.

(c) The direction of deflection gets reversed i.e., now it deflects towards west.

(d) An electric bell works on this principle.

For an ideal transformer, when there is no energy loss, the output power will be equal to the input power. i.e., power in secondary coil = power in primary coil or E_sI_s = E_pI_p

Assumption made is that the resistance is negligible and there is no energy loss.

Given,

• Number of turns (N) = 100 turns
• Decrease in the flux = 5 milli weber (0.005 weber to 0 weber),
• Time = 5 second

From relation,

e.m.f. induced e = N × rate of increase of magnetic flux

Substituting the values in the formula we get,

$$\begin{aligned}\text e = 100 \times \frac{0.005}{5} \\[1em] = 0.1\ \text V\end{aligned}$$

Hence, the e.m.f. induced in the coil is 0.1 V or 100 m V.

Given,

• N_p = 800
• N_s = 8
• E_p = 220 V
• E_s = ?

Now,

$\frac{\text E_\text s}{\text E_\text p} = \frac{\text N_\text s}{\text N_\text p}$

Substituting the values in the formula we get,

$$\begin{aligned}\frac{\text E_\text s}{220} = \frac{8}{800} \\[1em] \Rightarrow \text E_\text s = 220 \times \frac{8}{800} \\[1em] = 2.2\ \text V\end{aligned}$$

Hence, output voltage = 2.2 V

Given,

• E_s = 8 V
• E_p = 240 V
• N_p = 4800
• N_s = ?

We know that,

Now,

$\frac{\text E_\text s}{\text E_\text p} = \frac{\text N_\text s}{\text N_\text p}$

Substituting the values in the formula we get,

$$\begin{aligned}\frac{8}{240} = \frac{\text N_\text s}{4800} \\[1em] \Rightarrow \text N_\text s = 4800 \times \frac{8}{240} \\[1em] = 160\end{aligned}$$

Hence, the number of turns in the secondary coil is 160.

(a) Given,

• E_p = 220 V
• E_S = 44 V

Now,

$\frac{\text E_\text s}{\text E_\text p} = \frac{\text N_\text s}{\text N_\text p}$

Substituting the values in the formula we get,

$$\begin{aligned}\frac{44}{220} = \frac{\text N_\text s}{\text N_\text p} \\[1em] \Rightarrow \frac{\text N_\text s}{\text N_\text p} = \frac{44}{220} \\[1em] = \frac{1}{5}\end{aligned}$$

Hence, turns ratio = 1 : 5

(b)

• I_s = 2 A
• I_p = ?

From relation,

${\text E_\text s}{\text I_\text s} = {\text E_\text p}{\text I_\text p}$

Substituting the values in the formula we get,

$$\begin{aligned}44 \times 2 = 220 \times \text I_\text p \\[1em] \Rightarrow \text I_\text p = \frac{44 \times 2}{220} \\[1em] = 0.4\ \text A\end{aligned}$$

Hence, input current = 0.4 A

Since the supply voltage (220 V) is much higher than the required voltage (11 V), the student needs a step down transformer to reduce the voltage.

Given,

• E_p = 220 V
• E_s = 11 V

Let number of turns at primary coil be N_p and at secondary be N_s respectively.

Now,

Turn Ratio = $\frac{\text N_\text s}{\text N_\text p} = \frac{\text E_\text s}{\text E_\text p}=\frac{11}{220}=\frac{1}{20}$

Hence, recommended turn ratio should be $\frac{\textbf 1}{\textbf {20}}$.