Electromagnetic Induction Chapter-Wise Test 16

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil of 90 turns and area 0.03 m² is in a field that increases from 0 to 0.06 T in 0.3 s. What is the induced emf?

\( \Delta \Phi = B A = 0.06 \times 0.03 = 0.0018 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 90 \times \frac{0.0018}{0.3} = 90 \times 0.006 = 0.54 \, \text{V} \).

0.4 V
0.5 V
0.54 V
0.6 V
2

A coil is placed in a magnetic field that increases in strength. The energy stored in the coil’s magnetic field comes from what source?

The energy stored (\( \frac{1}{2} L I^2 \)) comes from the work done by the external source (e.g., a battery) against the back emf to establish the current.

Magnetic field itself
Thermal energy of the coil
Electrostatic potential
Work done by an external source
4

A coil of self-inductance 0.8 H has its current decreased from 6 A to 3 A in 0.2 s. What is the magnitude of the induced emf?

\( \varepsilon = L \frac{\Delta I}{\Delta t} \).

\( \Delta I = 3 - 6 = -3 \, \text{A} \), \( \Delta t = 0.2 \, \text{s} \).

\( \varepsilon = 0.8 \times \frac{-3}{0.2} = 0.8 \times (-15) = -12 \, \text{V} \), magnitude = 12 V.

10 V
12 V
14 V
16 V
2

A solenoid of 900 turns/m and area 0.015 m² has \( \mu_r = 2 \). What is its self-inductance? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

\( L = \mu_r \mu_0 n^2 A l \), assume \( l = 1 \, \text{m} \).

\( L = 2 \times 4\pi \times 10^{-7} \times (900)^2 \times 0.015 \times 1 = 0.0305 \, \text{H} \approx 0.03 \, \text{H} \).

0.02 H
0.025 H
0.03 H
0.035 H
3

A square loop of side 18 cm rotates at 10 rad/s in a 0.25 T field. What is the maximum emf induced?

\( A = (0.18)^2 = 0.0324 \, \text{m}^2 \).

\( \varepsilon_0 = N B A \omega = 1 \times 0.25 \times 0.0324 \times 10 = 0.081 \, \text{V} \).

0.06 V
0.081 V
0.09 V
0.1 V
2

A loop of 0.45 m × 0.2 m moves out of a 0.6 T field at 1.5 m/s along its longer side. How long does the emf last?

Time = distance/velocity, distance = width along motion = 0.2 m.

\( t = \frac{0.2}{1.5} = 0.1333 \, \text{s} \approx 0.13 \, \text{s} \).

0.1 s
0.12 s
0.13 s
0.15 s
3

A circular loop of radius 11 cm is deformed into a straight wire in a 0.2 T field in 0.5 s. What is the induced emf?

Initial flux: \( \Phi = B A = 0.2 \times \pi \times (0.11)^2 = 0.0076 \, \text{Wb} \).

Final flux = 0.

\( \varepsilon = \frac{\Delta \Phi}{\Delta t} = \frac{0.0076}{0.5} = 0.0152 \, \text{V} \approx 0.015 \, \text{V} \).

0.01 V
0.015 V
0.02 V
0.025 V
2

A coil of 220 turns rotates at 70 rad/s in a 0.05 T field. If the area is 0.025 m², what is the maximum emf?

\( \varepsilon_0 = N B A \omega = 220 \times 0.05 \times 0.025 \times 70 = 19.25 \, \text{V} \).

18 V
18.5 V
19 V
19.25 V
4

A rectangular loop of sides 40 cm and 20 cm moves out of a 0.9 T field at 1 m/s perpendicular to the longer side. What is the motional emf?

\( \varepsilon = B l v \), \( l = 0.2 \, \text{m} \).

\( \varepsilon = 0.9 \times 0.2 \times 1 = 0.18 \, \text{V} \).

0.18 V
0.2 V
0.22 V
0.25 V
1

A solenoid of 250 turns and length 0.8 m induces an emf of 0.75 V in a nearby coil when its current changes from 0 to 2.5 A in 0.25 s. What is the mutual inductance?

\( \varepsilon = M \frac{\Delta I}{\Delta t} \).

\( \Delta I = 2.5 - 0 = 2.5 \, \text{A} \), \( \Delta t = 0.25 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{0.75}{\frac{2.5}{0.25}} = \frac{0.75}{10} = 0.075 \, \text{H} \).

0.075 H
0.09 H
0.1 H
0.12 H
1

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