Electromagnetic Induction Chapter-Wise Test 8

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A coil with \( L = 0.25 \, \text{H} \) has its current increased from 0 to 4 A in 0.4 s. What is the energy stored?

\( W = \frac{1}{2} L I^2 = \frac{1}{2} \times 0.25 \times (4)^2 = 0.125 \times 16 = 2 \, \text{J} \).

1.5 J
1.8 J
1.9 J
2 J
4

A solenoid of 400 turns per meter and area 0.015 m² has a current drop from 5 A to 2 A in 0.3 s. What is the self-induced emf? (\( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \))

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

\( L = 4\pi \times 10^{-7} \times (400)^2 \times 0.015 \times 1 = 0.003016 \, \text{H} \).

\( \varepsilon = L \frac{\Delta I}{\Delta t} = 0.003016 \times \frac{2 - 5}{0.3} = 0.003016 \times (-10) = 0.03016 \, \text{V} \approx 0.03 \, \text{V} \).

0.02 V
0.03 V
0.04 V
0.05 V
2

A coil of 100 turns and area 0.03 m² is in a 0.08 T field that drops to zero in 0.2 s. What is the induced emf?

\( \Delta \Phi = B A = 0.08 \times 0.03 = 0.0024 \, \text{Wb} \).

\( \varepsilon = N \frac{\Delta \Phi}{\Delta t} = 100 \times \frac{0.0024}{0.2} = 100 \times 0.012 = 1.2 \, \text{V} \).

0.8 V
1.0 V
1.2 V
1.4 V
3

A conducting rod is rotated about one end in a uniform magnetic field. The emf induced between the ends is due to what fundamental effect?

The rotation causes charges to move through the field, experiencing a magnetic force (Lorentz force) that separates them, inducing an emf along the rod.

Electrostatic induction
Change in field strength
Magnetic force on moving charges
Thermal agitation
3

A solenoid of 300 turns and length 0.6 m induces an emf of 0.9 V in a nearby coil when its current changes from 1 A to 3 A in 0.3 s. What is the mutual inductance?

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

\( \Delta I = 3 - 1 = 2 \, \text{A} \), \( \Delta t = 0.3 \, \text{s} \).

\( M = \frac{\varepsilon}{\frac{\Delta I}{\Delta t}} = \frac{0.9}{\frac{2}{0.3}} = \frac{0.9}{6.67} \approx 0.135 \, \text{H} \).

0.135 H
0.15 H
0.18 H
0.2 H
1

A solenoid of 950 turns/m and area 0.016 m² has \( \mu_r = 1 \). 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 \( l = 1 \, \text{m} \).

\( L = 1 \times 4\pi \times 10^{-7} \times (950)^2 \times 0.016 \times 1 = 0.01815 \, \text{H} \approx 0.018 \, \text{H} \).

0.015 H
0.016 H
0.018 H
0.02 H
3

A rectangular loop of sides 45 cm and 25 cm moves out of a 1.0 T field at 0.8 m/s perpendicular to the longer side. What is the motional emf?

\( \varepsilon = B l v \), \( l = 0.25 \, \text{m} \).

\( \varepsilon = 1.0 \times 0.25 \times 0.8 = 0.2 \, \text{V} \).

0.2 V
0.25 V
0.3 V
0.35 V
1

A rectangular loop of sides 12 cm and 4 cm moves out of a 0.35 T field at 2 m/s perpendicular to the longer side. What is the motional emf?

\( \varepsilon = B l v \), \( l = 0.04 \, \text{m} \).

\( \varepsilon = 0.35 \times 0.04 \times 2 = 0.028 \, \text{V} \).

0.028 V
0.032 V
0.036 V
0.04 V
1

A solenoid with mutual inductance 0.18 H has a current change of 5 A/s in the primary coil. What is the induced emf in the secondary coil?

\( \varepsilon = M \frac{dI}{dt} = 0.18 \times 5 = 0.9 \, \text{V} \).

0.6 V
0.8 V
0.9 V
1.0 V
3

A coil of self-inductance 1.5 H has its current decreased from 7 A to 4 A in 0.3 s. What is the magnitude of the induced emf?

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

\( \Delta I = 4 - 7 = -3 \, \text{A} \), \( \Delta t = 0.3 \, \text{s} \).

\( \varepsilon = 1.5 \times \frac{-3}{0.3} = 1.5 \times (-10) = -15 \, \text{V} \), magnitude = 15 V.

12 V
15 V
18 V
20 V
2

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