Question 1

The emf produced by an ac generator is given by ε = ωNBA sin ωt. In SI units, what is the value of ω for a frequency of 60.0 Hz?
A) 60.0 Hz
B) 120 rad/s
C) 2.00π rad/s
D) 377 rad/s
E) 377 Hz

Accepted Answer

The frequency of the generator is given as 60.0 Hz. We know that the angular frequency (ω) is related to the frequency (f) by the equation ω = 2πf. Therefore, ω = 2π(60.0 Hz) = 377 rad/s.

Question 2

If the rotation rate of a generator coil is doubled, what happens to the peak emf?
A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It quarters.

Accepted Answer

The peak emf is directly proportional to the rate of change of magnetic flux, which is given by the equation E=-(dФ/dt). Since the rotation rate of the coil is doubled, the rate of change of magnetic flux also doubles, resulting in a doubling of the peak emf.

Question 3

Faraday's law of induction states that the emf induced in a rectangular loop of wire is proportional to
A) the magnetic flux.
B) the rate of change of the magnetic flux.
C) current divided by the time.
D) the magnetic flux density times the area of the loop.

Accepted Answer

Faraday's law of induction states that the emf induced in a loop of wire is proportional to the rate of change of the magnetic flux passing through the loop. Therefore, choice B is the correct answer. Choice A is partially correct, as the emf is also proportional to the magnetic flux, but only the rate of change of the flux is considered in the law. Choice C is incorrect, as it refers to the definition of average current, and choice D is also incorrect, as it refers to the magnetic flux through the loop, not the rate of change of the flux.

Question 4

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the field has a value of 0.25 T, what is the total flux through the coil? A) 0.0 B) 5.0 × 10^-3 T·m² C) 25 × 10^-5 T·m² D) 50 T·m² E) 25 T·m²

Accepted Answer

The magnetic flux ($\Phi$) through a coil is given by the formula $\Phi = NBA$, where $N$ is the number of turns in the coil, $B$ is the magnetic field strength, and $A$ is the area of the coil. Given $N = 20$, $B = 0.25$ T, and $A = 10 \times 10^{-4}$ m$^2$ (since $10$ cm$^2$ = $10 \times 10^{-4}$ m$^2$), the total flux is $\Phi = 20 \times 0.25 \times 10 \times 10^{-4} = 5.0 \times 10^{-3}$ T·m$^2$.

Question 5

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the potential difference between the ends of the rod?
A) 12 mV
B) 60 mV
C) 30 mV
D) 15 mV
E) 0 mV

Accepted Answer

The potential difference between the ends of the rod is given by the equation:

V = BLv

where B is the magnitude of the magnetic field, L is the length of the rod, and v is the velocity of the rod.

Plugging in the given values, we get:

V = (5.0 x 10^-3 T)(2.0 m)(6.0 m/s) = 60 mV

Therefore, the potential difference between the ends of the rod is 60 mV, which corresponds to choice B.

Question 6

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnitude of the electric field in the rod?
A) 12 mV/m
B) 60 mV/m
C) 30 mV/m
D) 15 mV/m
E) 0.0 mV/m

Accepted Answer

The magnitude of the electric field (E) induced in the rod can be calculated using the formula E = vB, where v is the velocity of the rod and B is the magnetic field. Substituting the given values: E = 6.0 m/s * 5.0 mT = 30 mV/m.

Question 7

A coil is rotated in a magnetic field about an axis perpendicular to both the field and the coil axis (normal to the coil area). During each rotation, how many times does the flux through the coil equal zero?
A) 0
B) 1
C) 2
D) 4
E) more than 4

Accepted Answer

The flux through the coil equals zero twice during each rotation. This occurs when the plane of the coil is parallel to the magnetic field lines, allowing no field lines to pass through the coil. This situation happens twice in a full 360-degree rotation.

Question 8

The ac motor and generator were invented by
A) Thomas Edison.
B) Nikola Tesla.
C) George Westinghouse.
D) James Clerk Maxwell.
E) Heinrich Hertz.

Accepted Answer

Nikola Tesla is credited with inventing the alternating current (AC) motor and generator, which revolutionized the electric power industry. Edison, Westinghouse, Maxwell, and Hertz all made important contributions to the field of electricity, but they did not invent the AC motor and generator.

Question 9

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnetic flux swept through per second by the rod? A) 0.0 B) 15 mT·m² C) 30 mT·m² D) 60 mT·m² E) 12 mT·m²

Accepted Answer

The answer of A metal rod of length 2.0 m...

Question 10

A conducting rod is free to slide on horizontal, frictionless rails separated by 2.0 m. At a particular time, the rod is sliding at 4.0 m/s to the right, as shown. A uniform magnetic field is directed into the page. If a current of 40 mA is generated in the circuit at this time, and the resistance R is 0.36 Ω, what is the magnitude of the magnetic field between the rails? 
A) 0.028 T
B) 0.11 T
C) 14 mT
D) 3.6 mT
E) 1.8 mT

Accepted Answer

The answer of A conducting rod is free to slide...

Question 11

The SI unit H (the henry) is equal to a
A) V/m.
B) V/A.
C) V·s.
D) V·s/A.
E) V·A/s.

Accepted Answer

The henry (H) is the SI unit of inductance. Inductance is defined as the ratio of voltage to current in a circuit, measured in volts per ampere (V/A). However, the unit H is defined as V·s/A, which can be rearranged to V·s/A = (V/A)·s = H. Therefore, the correct choice is D.

Question 12

A flat coil has a maximum flux of 4.0 × 10^-3 T·m² through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated 60^° (so that its normal makes a 60^° angle with the field), what is the flux through it? A) 4.0 × 10^-3 T·m² B) 8.0 × 10^-3 T·m² C) 3.5 × 10^-3 T·m² D) 2.0 × 10^-3 T·m² E) 6.9 × 10^-3 T·m²

Accepted Answer

The magnetic flux through a coil is given by $\Phi = B \cdot A \cdot \cos(\theta)$, where $B$ is the magnetic field strength, $A$ is the area of the coil, and $\theta$ is the angle between the magnetic field and the normal to the coil. At $60^\circ$, $\cos(60^\circ) = 0.5$. Therefore, the flux is halved from its maximum value of $4.0 \times 10^{-3} \, \text{T}\cdot\text{m}^2$, resulting in $2.0 \times 10^{-3} \, \text{T}\cdot\text{m}^2$.

Question 13

A metal rod of length L moves with velocity v, perpendicular to its length, in a magnetic field B, which is perpendicular to both the rod and its velocity. If the length of the rod is doubled, what happens to the electric field in the rod?
A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It quarters.

Accepted Answer

The electric field in the rod is proportional to the velocity and the magnetic field, but not affected by the length of the rod. Therefore, if the length is doubled, the electric field remains the same.

Question 14

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the magnitude of the field increases from 0.25 T to 0.35 T in 2.0 s, what is the average emf induced in the coil? A) 7.0 mV B) 2.0 mV C) 1.0 mV D) 3.5 mV E) 4.0 mV

Accepted Answer

The answer of A 20 turn coil of area 10...

Question 15

A conducting rod is free to slide on horizontal metal rails without friction. At a particular time, it is sliding with velocity v to the right, as shown. A uniform magnetic field B is directed into the page, the separation of the rails is L, and the resistance of the circuit is R. In what direction in the diagram is the current flowing in the resistor at this time? 
A) up
B) down
C) up then down
D) down then up
E) Insufficient information given.

Accepted Answer

The answer of A conducting rod is free to slide...

Question 16

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. If the resistance of the rod is 15 mΩ, what is the current in the rod?
A) 0.0 A
B) 1.0 A
C) 2.0 A
D) 4.0 A
E) 8.0 A

Accepted Answer

The magnetic force experienced by the rod can be calculated using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the rod. Since the velocity of the rod is perpendicular to the magnetic field and the rod, there is no force on the rod. Therefore, the current in the rod is zero.

Question 17

A conducting rod is free to slide horizontally on frictionless rails separated by 2.0 m. At a particular time, the rod is sliding at 3.0 m/s to the right, as shown. There is a uniform magnetic field of magnitude 0.66 mT directed into the page. If the resistance R is 220 mΩ, what is the current in the circuit at this time? 
A) 18 mA
B) 9.0 mA
C) 87 μA
D) 3.0 μA
E) 4.5 mA

Accepted Answer

The answer of A conducting rod is free to slide...

Question 18

The unit of magnetic flux is the weber. 1 Wb equals A) 1 V·m. B) 1 V·s/A. C) 1 T·m². D) π lines/m².

Accepted Answer

1 Weber (Wb) is equivalent to 1 Tesla meter squared (1 T·m^2), which is the unit of magnetic flux. This represents the product of a magnetic field (Tesla) and the area through which the field is passing (square meters).

Question 19

A generator has 200 turns of wire on a coil of radius 2.00 cm. What rotational speed is necessary to produce an emf of amplitude 4.50 V if the magnetic field in the region of the coil is 0.180 T?
A) 60.0 rad/s
B) 16.0 rpm
C) 100 rpm
D) 500 rpm
E) 950 rpm

Accepted Answer

The emf amplitude is given by the formula: emf = NABωsin(ωt), where N is the number of turns, A is the area of the coil, B is the magnetic field, and ω is the angular velocity. Solving for ω, we find ω = emf / (NAB). Substituting the given values, we calculate ω and convert it to rpm, resulting in approximately 950 rpm.

Question 20

For the typical household electricity in the United States and Canada, what is the amplitude of the provided emf?
A) 120 V
B) 240 V
C) 60.0 V
D) 170 V
E) 330 V

Accepted Answer

The typical household electricity in the United States and Canada is supplied at 120 V RMS (root mean square), which corresponds to an amplitude of approximately 170 V. This is because the RMS value of a sinusoidal voltage, like that supplied to households, is its peak (or amplitude) value divided by the square root of 2.

Quiz 20: Electromagnetic Induction

The emf produced by an ac generator is given by ε = ωNBA sin ωt. In SI units, what is the value of ω for a frequency of 60.0 Hz?

If the rotation rate of a generator coil is doubled, what happens to the peak emf?

Faraday's law of induction states that the emf induced in a rectangular loop of wire is proportional to

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the field has a value of 0.25 T, what is the total flux through the coil?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the potential difference between the ends of the rod?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnitude of the electric field in the rod?

A coil is rotated in a magnetic field about an axis perpendicular to both the field and the coil axis (normal to the coil area) . During each rotation, how many times does the flux through the coil equal zero?

The ac motor and generator were invented by

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnetic flux swept through per second by the rod?

The SI unit H (the henry) is equal to a

A flat coil has a maximum flux of 4.0 × 10^-3 T·m² through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated 60^° (so that its normal makes a 60^° angle with the field) , what is the flux through it?

A metal rod of length L moves with velocity v, perpendicular to its length, in a magnetic field B, which is perpendicular to both the rod and its velocity. If the length of the rod is doubled, what happens to the electric field in the rod?

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the magnitude of the field increases from 0.25 T to 0.35 T in 2.0 s, what is the average emf induced in the coil?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. If the resistance of the rod is 15 mΩ, what is the current in the rod?

The unit of magnetic flux is the weber. 1 Wb equals

A generator has 200 turns of wire on a coil of radius 2.00 cm. What rotational speed is necessary to produce an emf of amplitude 4.50 V if the magnetic field in the region of the coil is 0.180 T?

For the typical household electricity in the United States and Canada, what is the amplitude of the provided emf?

Quiz 20: Electromagnetic Induction

The emf produced by an ac generator is given by ε = ωNBA sin ωt. In SI units, what is the value of ω for a frequency of 60.0 Hz?

If the rotation rate of a generator coil is doubled, what happens to the peak emf?

Faraday's law of induction states that the emf induced in a rectangular loop of wire is proportional to

A 20 turn coil of area 10 cm2 is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the field has a value of 0.25 T, what is the total flux through the coil?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the potential difference between the ends of the rod?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnitude of the electric field in the rod?

A coil is rotated in a magnetic field about an axis perpendicular to both the field and the coil axis (normal to the coil area) . During each rotation, how many times does the flux through the coil equal zero?

The ac motor and generator were invented by

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. What is the magnetic flux swept through per second by the rod?

The SI unit H (the henry) is equal to a

A flat coil has a maximum flux of 4.0 × 10-3 T·m2 through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated 60° (so that its normal makes a 60° angle with the field) , what is the flux through it?

A metal rod of length L moves with velocity v, perpendicular to its length, in a magnetic field B, which is perpendicular to both the rod and its velocity. If the length of the rod is doubled, what happens to the electric field in the rod?

A 20 turn coil of area 10 cm2 is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the magnitude of the field increases from 0.25 T to 0.35 T in 2.0 s, what is the average emf induced in the coil?

A metal rod of length 2.0 m is moved at 6.0 m/s in a direction perpendicular to its length. A 5.0 mT magnetic field is perpendicular to both the rod and its velocity. If the resistance of the rod is 15 mΩ, what is the current in the rod?

The unit of magnetic flux is the weber. 1 Wb equals

A generator has 200 turns of wire on a coil of radius 2.00 cm. What rotational speed is necessary to produce an emf of amplitude 4.50 V if the magnetic field in the region of the coil is 0.180 T?

For the typical household electricity in the United States and Canada, what is the amplitude of the provided emf?

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the field has a value of 0.25 T, what is the total flux through the coil?

A flat coil has a maximum flux of 4.0 × 10^-3 T·m² through it, with its area perpendicular to a uniform magnetic field. When the coil is rotated 60^° (so that its normal makes a 60^° angle with the field) , what is the flux through it?

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to the coil's area is in the same direction as the field. If the magnitude of the field increases from 0.25 T to 0.35 T in 2.0 s, what is the average emf induced in the coil?