Grade 12 : Physics - Electromagnetic Induction (Set 3)

Question 1

A square conducting loop with side length $L = 0.2 m$ is oriented perpendicular to a magnetic field changing with time according to $B(t) = 3t^2 + 2t + 1 ext{ T}$.

Calculate the magnitude of the induced electromotive force (EMF) in the loop at time $t = 2 ext{ s}$.

Accepted Answer

B) 0.56 V

Answer

A) 0.28 V

Answer

C) 1.12 V

Answer

D) 0.44 V

Answer

E) 0.84 V

Question 2

An AC generator armature consists of a circular coil of $N = 100$ turns, each of radius $r = 0.1 m$. The coil rotates at a constant angular frequency $\omega = 60 ext{ rad/s}$ in a uniform magnetic field $B = 0.05 ext{ T}$.

What is the peak electromotive force (EMF) generated across the terminals of the coil?

Accepted Answer

C) $30\pi	ext{ V}$

Answer

A) $15\pi	ext{ V}$

Answer

B) $20\pi	ext{ V}$

Answer

D) $60\pi	ext{ V}$

Answer

E) $10\pi	ext{ V}$

Question 3

A conducting rod of length $l = 0.5 m$ moves to the right at a constant velocity $v = 4 m/s$ on frictionless parallel rails of resistance $R = 2\ \Omega$. The system is in a uniform magnetic field $B = 0.5 ext{ T}$ directed vertically into the page.

Find the magnitude and direction of the induced current flowing through the rod.

Accepted Answer

A) 0.5 A, counterclockwise

Answer

B) 0.5 A, clockwise

Answer

C) 1.0 A, counterclockwise

Answer

D) 1.0 A, clockwise

Answer

E) 2.0 A, counterclockwise

Question 4

An inductor with self-inductance $L = 50 ext{ mH}$ carries a current that decreases uniformly from $I_1 = 4 ext{ A}$ to $I_2 = 1 ext{ A}$ over a time interval $\Delta t = 0.03 ext{ s}$.

What is the average self-induced EMF across the inductor during this interval?

Accepted Answer

C) 5.0 V

Answer

A) 2.5 V

Answer

B) 3.5 V

Answer

D) 7.5 V

Answer

E) 10.0 V

Question 5

Two coaxial coils have a mutual inductance $M = 0.2 ext{ H}$. The primary current changes with time according to $I_1(t) = 5\sin(100\pi t) ext{ A}$.

Determine the peak value of the induced EMF in the secondary coil.

Accepted Answer

D) $100\pi	ext{ V}$

Answer

A) $50\pi	ext{ V}$

Answer

B) $200\pi	ext{ V}$

Answer

C) $20\pi	ext{ V}$

Answer

E) $500\pi	ext{ V}$

Question 6

A high-power inductor with self-inductance $L = 0.8 ext{ H}$ operates at a steady current of $I = 5 ext{ A}$.

Calculate the magnetic potential energy stored in the magnetic field of the inductor.

Accepted Answer

E) 10 J

Answer

A) 5 J

Answer

B) 20 J

Answer

C) 40 J

Answer

D) 2.5 J

Question 7

An airplane with a wingspan of $l = 30 m$ flies horizontally at a velocity of $v = 250 m/s$ over a geographic region where the vertical component of Earth's magnetic field is $B_v = 4 imes 10^{-5} ext{ T}$.

What is the potential difference induced between the tips of the airplane's wings?

Accepted Answer

A) 0.30 V

Answer

B) 0.15 V

Answer

C) 0.60 V

Answer

D) 1.20 V

Answer

E) 0.03 V

Question 8

A uniform metallic rod of length $L = 1.0 m$ rotates in a horizontal plane about one fixed pivot end with a constant angular speed $\omega = 20 ext{ rad/s}$ perpendicular to a vertical magnetic field $B = 0.4 ext{ T}$.

Find the induced EMF generated between the pivot end and the rotating tip of the rod.

Accepted Answer

B) 4.0 V

Answer

A) 2.0 V

Answer

C) 8.0 V

Answer

D) 1.0 V

Answer

E) 16.0 V

Question 9

An ideal LC resonant circuit consists of a pure inductor $L = 20 ext{ mH}$ and a capacitor $C = 50\mu ext{F}$.

Calculate the natural angular frequency $\omega_0$ of free electromagnetic oscillations in the circuit.

Accepted Answer

C) 1000 rad/s

Answer

A) 500 rad/s

Answer

B) 2000 rad/s

Answer

D) 100 rad/s

Answer

E) 5000 rad/s

Question 10

Statement I: When a solid metal block is moved through a non-uniform magnetic field, induced circular currents called eddy currents are produced, resulting in electromagnetic damping.
Statement II: According to Lenz's law, eddy currents flow in directions that assist and accelerate the relative motion of the conductor.

Which of the following evaluations of Statement I and Statement II is correct?

Accepted Answer

B) Statement I is correct but Statement II is incorrect.

Answer

A) Both Statement I and Statement II are correct.

Answer

C) Statement I is incorrect but Statement II is correct.

Answer

D) Both Statement I and Statement II are incorrect.

Question 11

Time $t ext{ (s)}$	Magnetic Flux $\Phi ext{ (mWb)}$
0.0	4.0
1.0	10.0
2.0	16.0
3.0	22.0

The magnetic flux passing through a coil of $N = 50$ turns varies linearly as recorded in the table above. Calculate the magnitude of the constant induced EMF in the coil.

Accepted Answer

D) 0.30 V

Answer

A) 0.15 V

Answer

B) 0.60 V

Answer

C) 3.00 V

Answer

E) 0.03 V

Question 12

A long straight solenoid of radius $R_1 = 0.1 m$ has $n$ turns per unit length such that $\mu_0 n = 2 imes 10^{-3} ext{ T/A}$. The current increases as $I(t) = 5t ext{ A}$. A circular wire loop of radius $R_2 = 0.2 m$ surrounds the solenoid coaxially.

Determine the magnitude of the EMF induced in the outer wire loop.

Accepted Answer

A) $0.10\pi	ext{ mV}$

Answer

B) $0.05\pi	ext{ mV}$

Answer

C) $0.20\pi	ext{ mV}$

Answer

D) $0.40\pi	ext{ mV}$

Answer

E) $0.50\pi	ext{ mV}$

Question 13

A circuit consists of an inductor $L = 0.4 ext{ H}$ and a resistor $R = 20\ \Omega$ connected in series with a constant DC voltage source $V = 12 ext{ V}$.

What are the inductive time constant $ au$ of the circuit and the steady-state maximum current $I_0$?

Accepted Answer

B) $	au = 20	ext{ ms},\ I_0 = 0.6	ext{ A}$

Answer

A) $	au = 10	ext{ ms},\ I_0 = 0.6	ext{ A}$

Answer

C) $	au = 20	ext{ ms},\ I_0 = 1.2	ext{ A}$

Answer

D) $	au = 50	ext{ ms},\ I_0 = 0.3	ext{ A}$

Answer

E) $	au = 40	ext{ ms},\ I_0 = 0.6	ext{ A}$

Question 14

A conducting circular loop of radius $r = 0.5 m$ lies in the xy-plane. A spatially uniform magnetic field directed along the $+z$-axis decays exponentially according to $B(t) = B_0 e^{-t/ au}$, where $B_0 = 2.0 ext{ T}$ and $ au = 4.0 ext{ s}$.

Calculate the magnitude of the induced electric field $E$ along the perimeter of the loop at time $t = 0$.

Accepted Answer

C) 0.125 V/m

Answer

A) 0.0625 V/m

Answer

B) 0.250 V/m

Answer

D) 0.500 V/m

Answer

E) 1.000 V/m

Question 15

Two coupled inductors have self-inductances $L_1 = 80 ext{ mH}$ and $L_2 = 20 ext{ mH}$. When placed close together, their measured mutual inductance is $M = 32 ext{ mH}$.

Calculate the coupling coefficient $K$ between the two coils.

Accepted Answer

D) 0.8

Answer

A) 0.4

Answer

B) 0.6

Answer

C) 0.9

Answer

E) 0.5

Question 16

A square loop of side length $a = 0.1 m$ and electrical resistance $R = 5\ \Omega$ rotates at a constant angular speed $\omega = 100 ext{ rad/s}$ in a uniform magnetic field $B = 0.5 ext{ T}$.

Calculate the peak electrical power dissipated in the loop during rotation.

Accepted Answer

E) 50 mW

Answer

A) 25 mW

Answer

B) 100 mW

Answer

C) 10 mW

Answer

D) 75 mW

Question 17

A square loop of side length $s = 0.2 m$ enters a uniform magnetic field region $B = 1.5 ext{ T}$ at a constant velocity $v = 3 m/s$. Total circuit resistance of the loop is $R = 0.9\ \Omega$.

Calculate the magnitude of the retarding magnetic force acting on the loop as it enters the field.

Accepted Answer

A) 0.30 N

Answer

B) 0.15 N

Answer

C) 0.60 N

Answer

D) 0.90 N

Answer

E) 0.45 N

Question 18

A flat circular coil of $N = 200$ turns has cross-sectional area $A = 50 cm^2 = 5 imes 10^{-3} m^2$ and total resistance $R = 20\ \Omega$. A magnetic field perpendicular to the coil plane drops from $B_1 = 0.8 ext{ T}$ to $B_2 = 0.2 ext{ T}$.

Determine the total electric charge $\Delta Q$ that flows through the coil during this magnetic flux change.

Accepted Answer

B) 30 mC

Answer

A) 15 mC

Answer

C) 60 mC

Answer

D) 10 mC

Answer

E) 45 mC

Question 19

An ideal step-down transformer operates with primary voltage $V_p = 220 ext{ V}$ and has $N_p = 1100$ turns in the primary winding and $N_s = 50$ turns in the secondary winding. The secondary load draws $I_s = 4.4 ext{ A}$.

Calculate the secondary voltage $V_s$ and the primary current $I_p$.

Accepted Answer

C) $V_s = 10	ext{ V},\ I_p = 0.2	ext{ A}$

Answer

A) $V_s = 20	ext{ V},\ I_p = 0.4	ext{ A}$

Answer

B) $V_s = 10	ext{ V},\ I_p = 0.5	ext{ A}$

Answer

D) $V_s = 5	ext{ V},\ I_p = 0.1	ext{ A}$

Answer

E) $V_s = 15	ext{ V},\ I_p = 0.3	ext{ A}$

Question 20

A conducting rod of mass $m = 0.1 kg$ slides down frictionless inclined parallel rails separated by width $w = 0.4 m$ in a uniform magnetic field $B = 0.5 ext{ T}$ directed perpendicular to the inclined plane (angle of inclination $ heta = 30^\circ$). Circuit resistance is $R = 2.0\ \Omega$ and $g = 10 m/s^2$.

Determine the terminal velocity $v_t$ reached by the falling rod.

Accepted Answer

D) 25 m/s

Answer

A) 10 m/s

Answer

B) 15 m/s

Answer

C) 20 m/s

Answer

E) 30 m/s

Set 3Grade 12 : Physics - Electromagnetic Induction