Question 1

Electric fields that arise from changing magnetic fields have all the properties below except
A) they terminate on electric charges.
B) they cannot be described by an electric potential.
C) their field lines take the form of closed loops.
D) work done by the field along a closed path may be non-zero.

Accepted Answer

Electric fields arising from changing magnetic fields (as described by Faraday's Law of electromagnetic induction) do not terminate on electric charges. Instead, they form closed loops, unlike electrostatic fields which do terminate on charges.

Question 2

The principle of operation that transformers depend upon is the induction of current in the secondary windings due to
A) motion of the primary winding relative to the secondary.
B) a varying magnetic field.
C) interaction of the core with the windings.
D) a varying electric field.

Accepted Answer

Transformers work based on the principle of electromagnetic induction, where a varying magnetic field in the primary winding induces a current in the secondary winding. This current is proportional to the number of turns in the windings, and can be stepped up or down in voltage depending on the ratio of turns between the primary and secondary winding. The motion or interaction of the windings or core does not play a significant role in the operation of the transformer. A varying electric field would be more applicable to capacitors rather than transformers.

Question 3

An LR circuit is prepared for an experiment, initially with its switch open. The time constant is that time after switch closure at which the energy stored in the inductor reaches approximately what percentage of its final value?
A) 63%
B) 14%
C) 37%
D) 40%
E) 100%

Accepted Answer

The answer of An LR circuit is prepared for an...

Question 4

The induced emf in a straight segment of wire that moves through a region with a magnetic field depends on all of the following, except
A) the orientation of the wire with respect to the magnetic field direction.
B) the length of the wire.
C) the resistance of the wire.
D) speed of the wire.
E) the magnetic field strength.

Accepted Answer

The induced emf in a wire moving through a magnetic field depends on the magnetic field strength, the speed of the wire, the length of the wire, and the orientation of the wire with respect to the magnetic field direction. The resistance of the wire does not affect the induced emf, but it does affect the current that flows in the wire due to the induced emf.

Question 5

Lenz's law arises because of the following basic principle
A) Gauss's law.
B) the conservation of momentum.
C) Coulomb's law.
D) the conservation of energy.
E) the conservation of charge.

Accepted Answer

Lenz's law is a consequence of the conservation of energy, specifically the law of conservation of energy. The law states that the direction of an induced current is such that it opposes the change causing it. This ensures that the induced current does not increase the total energy of the system, but rather works to conserve it.

Question 6

A coiled loop of wire is in the field region between the poles of an electromagnet, with the axis of the coil aligned with the magnetic field. Which of the following things would NOT result in an induced EMF in the coil?
A) Rotation of the coil about an axis perpendicular to the coil axis
B) Pulling the coil partly out of the field region
C) Increasing or decreasing the current in the electromagnet
D) Flexing the coil and changing its shape, keeping the perimeter the same
E) None of these choices will work.

Accepted Answer

The answer of A coiled loop of wire is in...

Question 7

A loop of wire is moved through a region of uniform magnetic field. As it is moved, its orientation with respect to the magnetic field direction does not change. The induced current in the loop
A) depends on the shape of the loop.
B) depends on the magnitude of the field.
C) depends on the speed with which it is moved.
D) is zero.
E) depends on the acceleration of the loop.

Accepted Answer

The induced current in the loop is zero because the orientation of the loop with respect to the magnetic field direction does not change.

Question 8

A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The 1531 coils of the generator are circular with diameter 7.5 cm. What is the necessary magnetic field for the generator?
A) 0.0079 T
B) 0.30 T
C) 0.075 T
D) 0.24 T

Accepted Answer

The maximum emf produced by the generator is given by the equation:
$emf = NBA\omega\sin(\omega t)$
where N is the number of turns, B is the magnetic field, A is the area of the loop, ω is the angular frequency, and t is time.
We are given that emf = 170 V, N = 1531, A = (π/4)(7.5 cm)^2 = 44.18 cm^2 = 0.004418 m^2, and ω = 2π(3200 rpm/60 s/min) = 335.1 rad/s.
Solving for B, we get:
$B = \frac{emf}{N A \omega}$
$B = \frac{170 	ext{ V}}{1531 \cdot 0.004418 	ext{ m}^2 \cdot 335.1 	ext{ rad/s}} = \boxed{0.075	ext{ T}}$
Therefore, the best choice is (C).

Question 9

A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The coils of the generator are circular with diameter 7.50 cm. Assuming the magnetic field in the generator is 0.0750 T, what is the number of loops needed in the generator coil?
A) 160
B) 1530
C) 6120
D) 4810
E) 25

Accepted Answer

The maximum emf of a generator is given by $\mathcal{E}_{max} = NBA\omega$, where $N$ is the number of loops, $B$ is the magnetic field, $A$ is the area of the loop, and $\omega$ is the angular frequency. Solving for $N$ we get $N=\frac{\mathcal{E}_{max}}{BA\omega}$. Since the diameter is given, we need to find the radius and then find the area of the circular coil. The radius is half the diameter, so $r=3.75	ext{ cm} = 0.0375 	ext{ m}$. The area of the circular coil is $A=\pi r^2 = 1.767 	imes 10^{-3} 	ext{ m}^2$. Plugging in the given values we get $N=\frac{(170	ext{ V})}{(0.0750	ext{ T})(1.767 	imes 10^{-3} 	ext{ m}^2)(2\pi \cdot 3200 	ext{ rpm}/60)} \approx 1530$, which is closest to answer choice B.

Question 10

A square conducting loop is situated such that it is vertical, in the xz-plane. The Earth's gravitational field points downward (in the -z direction). The loop is dropped and maintains its orientation in the xz-plane. A magnetic field pointing in the +y direction exists and is uniform with respect to time, but it varies as a function of z: B_y(z) = B₀(10 m − z). The loop is dropped and allowed to fall under the influence of gravitation. You observe the loop from the +y direction (i.e., looking toward the −y direction). Which of the following occurs? A) The situation is unclear because we do not know the initial conditions. B) There is a clockwise induced current. C) There is a counter-clockwise induced current. D) There is no induced current.

Accepted Answer

The magnetic field decreases with increasing z (as the loop falls, z decreases, making the magnetic field stronger). According to Lenz's law, the induced current will oppose the change causing it, meaning it will try to decrease the magnetic field inside the loop. Viewed from the +y direction, a clockwise current would create a magnetic field opposing the increase, thus a clockwise induced current is correct.

Question 11

A conducting ring is placed such that it is lying flat in the xy-plane. A magnetic field exists in the +z direction, and its strength is decreasing with time. Which of the following occurs?
A) No current is induced in the ring.
B) A current is induced, in the counter-clockwise direction, as viewed from above the xy-plane.
C) The situation is unclear because we do not know the initial conditions.
D) A current is induced, in the clockwise direction as viewed from above the xy-plane.

Accepted Answer

According to Faraday's Law, a changing magnetic field induces an electromotive force (EMF) and hence a current in a closed circuit. The direction of the induced current is such that it produces a magnetic field opposing the change in the original magnetic field. In this case, since the magnetic field is decreasing with time, the induced current will produce a magnetic field in the +z direction, which is opposite to the original magnetic field. Applying the right-hand rule for current direction shows that the induced current will flow in a counter-clockwise direction, as viewed from above the xy-plane.

Question 12

An LR circuit is prepared for an experiment, initially with its switch open. The time constant is that time after switch closure at which the current reaches approximately what percentage of its final value?
A) 100%
B) 90%
C) 37%
D) 63%
E) 50%

Accepted Answer

The time constant of an LR circuit, given by the formula tau = L/R, is the time it takes for the current to reach 63% of its final value. Therefore, the answer is D.

Question 13

The maximum induced emf in a generator whose coils are rotating at 240 rpm is 35 V. If, instead, it is desired to generate a maximum emf of 45 V but with half the magnetic field, what rotation rate must be used?
A) 380 rpm
B) 190 rpm
C) 310 rpm
D) 165 rpm
E) 620 rpm

Accepted Answer

The induced emf ($E$) in a generator is directly proportional to the magnetic field strength ($B$) and the rotation rate ($n$). Mathematically, this can be expressed as $E \propto Bn$. Given that the maximum emf is to be increased from 35 V to 45 V (a factor of $45/35 = 1.29$) while the magnetic field is halved, the rotation rate must be increased by a factor of $2 \times 1.29 = 2.58$ to compensate. Therefore, the new rotation rate is $240 \, \text{rpm} \times 2.58 = 619.2 \, \text{rpm}$, which rounds to 620 rpm, option E.

Question 14

In a transformer, the relationship between the primary and secondary currents depends on all of the following quantities except
A) the number of turns in the primary and secondary windings.
B) the resistance of the windings.
C) the voltage in the primary winding.
D) the properties of the core material.

Accepted Answer

The answer of In a transformer, the relationship between the...

Quiz 20: Electromagnetic Induction

Electric fields that arise from changing magnetic fields have all the properties below except

The principle of operation that transformers depend upon is the induction of current in the secondary windings due to

An LR circuit is prepared for an experiment, initially with its switch open. The time constant is that time after switch closure at which the energy stored in the inductor reaches approximately what percentage of its final value?

The induced emf in a straight segment of wire that moves through a region with a magnetic field depends on all of the following, except

Lenz's law arises because of the following basic principle

A coiled loop of wire is in the field region between the poles of an electromagnet, with the axis of the coil aligned with the magnetic field. Which of the following things would NOT result in an induced EMF in the coil?

A loop of wire is moved through a region of uniform magnetic field. As it is moved, its orientation with respect to the magnetic field direction does not change. The induced current in the loop

A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The 1531 coils of the generator are circular with diameter 7.5 cm. What is the necessary magnetic field for the generator?

A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The coils of the generator are circular with diameter 7.50 cm. Assuming the magnetic field in the generator is 0.0750 T, what is the number of loops needed in the generator coil?

A conducting ring is placed such that it is lying flat in the xy-plane. A magnetic field exists in the +z direction, and its strength is decreasing with time. Which of the following occurs?

An LR circuit is prepared for an experiment, initially with its switch open. The time constant is that time after switch closure at which the current reaches approximately what percentage of its final value?

The maximum induced emf in a generator whose coils are rotating at 240 rpm is 35 V. If, instead, it is desired to generate a maximum emf of 45 V but with half the magnetic field, what rotation rate must be used?

In a transformer, the relationship between the primary and secondary currents depends on all of the following quantities except