Electromagnetic Induction

Practice Questions:

Question 41: moderate

A wheel with ten metallic spockes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth’s magnetic field at the place. If the magnitude of the field is 0.4 Gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to :

1. \[1.256\times 10^{-3} V\]

2. \[6.28\times 10^{-4} V\]

3. \[1.256\times 10^{-4} V\]

4. \[6.28\times 10^{-5} V\]

View Answer

Using the formula for induced e.m.f. in a rotating conductor:

e = \frac{1}{2} B \omega L^2 = \frac{1}{2} B (2\pi f) L^2

Substituting

e = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4\pi) \times (0.5)^2 = 6.28 \times 10^{-5}\text{ V}

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Question 42: easy

A coil resistance 20 Ω and inductance 5 H is connected with a 100 V battery. Energy stored in the coil will be :

1. 41.5 J

2. 62.50 J

3. 125 J

4. 250 J

View Answer

I = \frac{V}{R} = \frac{100}{20} = 5 \text{ A}

U = \frac{1}{2} L I^2 = \frac{1}{2} \times 5 \times 5^2 = 62.5 \text{ J}

Energy stored = 62.5 J

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Question 43: easy

A square coil ACDE with its plane vertical is released from rest in a horizontal uniform
magnetic field B of length 2L. The acceleration of the coil is :

1. less than g for all the time till the loop crosses the magnetic field completely

2. less than g when it enters the field and greater than g when it comes out of the field

3. g all the time

4. less than g when it enters and comes out of the field but equal to g when it is within the field

View Answer

The acceleration is less than ' $g$ when entering or leaving the field because the changing magnetic flux induces a current that creates an opposing upward force (Lenz's Law).

Once the coil is fully inside the uniform $2L$ field, the flux is constant, the induced current drops to zero, and the coil falls freely with acceleration equal to $g$ .

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Question 44: moderate

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced
current is developed in it, which varies with time as shown in figure. The magnitude of
change in flux through the coil in webers is:

1. 2

2. 4

3. 6

4. 8

View Answer

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Question 45: moderate

Two coils are at fixed locations. When coil 1 has no current and the current in coil 2 increases at the rate 15.0 A/s the emf in coil 1 in 25.0 mV, when coil 2 has no current and coil 1 has a current of 3.6 A, the flux linkage in coil 2 is:

1. 16 mWb

2. 10 mWb

3. 4.00 mWb

4. 6.00 mWb

View Answer

Based on the problem in your editor, here is the solution in 3 lines without using the $ symbol:

Find Mutual Inductance (M): M = Induced EMF / (rate of change of current) = 25.0 mV / 15.0 A/s = 1.667 mH.
Calculate Flux Linkage: Flux = M × Current = 1.667 mH × 3.6 A = 6.00 mWb.
Result: The flux linkage in coil 2 is 6.00 mWb (Option 4).

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Question 46: easy

Two circular coils can be arranged in any of the three situations shown in the figure. Their
mutual inductance will be :

1. maximum In situation (a)

2. maximum In situation (b)

3. maximum In situation (c)

4. the same in all situations

View Answer

Based on the visual arrangement of the coils, the mutual inductance is maximum in situation (a).

This is because the coils are placed co-axially (one above the other), allowing the maximum amount of magnetic flux from the primary coil to pass through the secondary coil, resulting in the highest coupling coefficient.

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Question 47: easy

A vertical bar magnet is dropped from position on the axis of a fixed metallic coil as shown in fig – I. In fig. II the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are a1 and a2 respectively then

1. a1 > g , a2 > g

2. a1 > g , a2 < g

3. a1 < g , a2 < g

4. a1 < g , a2 > g

View Answer

In both cases, relative motion between the magnet and the coil induces a current that creates a magnetic force opposing the motion (Lenz's Law). This upward retarding force reduces the downward acceleration below gravity ( $g$ ), resulting in $a_1 < g$ and $a_2 < g$ .

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Question 48: easy

Two identical coaxial circular loops carry a current i each circulating in the same direction. If the loops approach each other

1. the current in each will decrease

2. the current in each will increase

3. the current in each will remain the same

4. the current in one will increase and in other will decrease

View Answer

When two loops with current in the same direction approach each other, the magnetic flux through each loop increases. According to Lenz's Law, an induced current will arise to oppose this change, causing the current in both loops to decrease.

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Question 49: easy

Two coils X and Y are placed in a circuit such that a current changes by 2 A in coil X and the magnetic flux change of 0.4 Wb occurs in coil Y. The value of mutual inductance of coils is :

1. 0.2 H

2. 2 H

3. 0.5 H

4. 5 H

View Answer

The mutual inductance ( $M$ ) is calculated by the ratio of flux change in coil Y to the current change in coil X:

M = \frac{\Delta \phi_Y}{\Delta I_X} = \frac{0.4 \text{ Wb}}{2 \text{ A}}

$M = 0.2 \text{ H}$

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Question 50: easy

A small square loop of wire of side l is placed inside a large square loop of wire of side L ( L > l ). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to :

1. l / L

2. l² / L

3. L/l

4. L²/l

View Answer

The mutual inductance M is found by calculating the magnetic flux through the small loop due to the current $I$ in the large loop. Using the formula for the magnetic field at the center of a square loop, $B \propto \frac{I}{L}$ .

Since the small loop is much smaller than the large one \( $L \gg l$ )\, the field is approximately uniform across its area \ $A = l^2$ . The flux $\Phi = B \cdot A$ is therefore proportional to \ $\frac{I}{L} \cdot l^2$ .

Because $M = \frac{\Phi}{I}$ , the mutual inductance scales as:

M \propto \frac{l^2}{L}

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