Question 1

A conducting rod slides at 4.0 m/s on metal rails separated by 2.0 m.If a current of 40 mA is generated in the circuit with resistance of 0.36 $\Omega$,what is 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

E

Question 2

A coil is rotated in a magnetic field about an axis perpendicular to the field.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

When the coil is rotated, the flux through it will change sinusoidally. The flux will be zero twice in each cycle, once when the coil is perpendicular to the field (maximum rate of change of flux) and once when the coil is parallel to the field (minimum rate of change of flux). Therefore, the flux through the coil will equal zero twice during each rotation, or a total of 2 times.

Question 3

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, which is the property of a circuit element that opposes any change in current. Inductance is defined as the ratio of the voltage across an inductor (V) to the rate of change of the current through it (dI/dt). Thus, the units of inductance can be expressed as V·s/A, which is equivalent to V·s/A = (J/C)·s/C = J/A = H. Therefore, the correct answer is D, V·s/A.

Question 4

A conducting rod is sliding on metal rails with velocity v.A magnetic field B is into the paper,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? 
A) up
B) down
C) up then down
D) down then up
E) Insufficient information given,

Accepted Answer

As the conducting rod slides on the metal rails, it cuts through the magnetic field, which induces an EMF (electromotive force) in the rod according to Faraday's law. The direction of the induced EMF is given by Lenz's law, which states that the induced current flows in a direction that opposes the change in magnetic flux. In this case, since the magnetic field is into the paper and the rod is moving to the right, the induced current will flow in a direction such that it creates a magnetic field out of the paper to oppose the entering magnetic field. Using the right-hand rule for the direction of the induced current, we see that the current flows downward through the resistor. Therefore, the correct answer is B) down.

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 m T magnetic field is perpendicular to both the rod and its velocity.If the resistance of the rod is 15 m$\Omega$, 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 answer of A metal rod of length 2.0 m...

Question 6

For the typical "household ac voltage" of 120 V,what is the amplitude of the emf?
A) 120 V
B) 240 V
C) 60.0 V
D) 170 V
E) 330 V

Accepted Answer

The typical household AC voltage of 120 V refers to the root mean square (RMS) value. The amplitude (peak value) of the emf is calculated using the formula: Amplitude = RMS value × √2. Therefore, 120 V × √2 ≈ 170 V.

Question 7

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, in turn, is directly proportional to the rotational rate of the coil. Therefore, if the rotational rate is doubled, the peak emf will also double.

Question 8

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to its area is in the direction of the field.If the field originally has a value of 0.25 T that increases 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 9

The ac motor and generator were invented by
A) Edison.
B) Tesla.
C) Westinghouse.
D) Maxwell.
E) Hertz.

Accepted Answer

The AC motor and generator were invented by Nikola Tesla. While Thomas Edison did play a significant role in the development of the electrical power industry, he focused mainly on DC (direct current) technology and did not invent the AC motor or generator. Westinghouse was an important promoter of AC power, but did not invent the technology itself. Maxwell and Hertz made important contributions to the understanding of electromagnetism, but did not directly invent the AC motor or generator.

Question 10

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 m T 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

Accepted Answer

The potential difference (emf) induced in the rod can be calculated using the formula emf = B * v * L, where B is the magnetic field strength, v is the velocity, and L is the length of the rod. Substituting the given values: emf = 5.0 T * 6.0 m/s * 2.0 m = 60 V or 60 mV.

Question 11

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 answer of A generator has 200 turns of wire...

Question 12

A conducting rod slides at 3.0 m/s on metal rails separated by 2.0 m.The 0.66 m T magnetic field is into the paper.If the resistance is 220 m$\Omega$, what is the current in the circuit? 
A) 18 mA
B) 9.0 mA
C) 87 $\mu$A
D) 3.0 $\mu$A
E) 4.5 mA

Accepted Answer

The answer of A conducting rod slides at 3.0 m/s...

Question 13

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) $\pi$ lines/m².

Accepted Answer

1 Weber (Wb) is defined as the magnetic flux that, linking a circuit of one turn, produces an electromotive force of 1 volt if it is reduced to zero at a uniform rate in 1 second. It is equivalent to 1 Tesla (T) times 1 square meter (m²), hence 1 Wb = 1 T·m².

Question 14

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 induced in the rod is given by E = vB, which is independent of the length of the rod. Therefore, doubling the length of the rod does not change the electric field.

Question 15

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to its area is in the direction of 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 $\times$ 10^-3 T·m² C) 25 $\times$ 10^-5 T·m² D) 50 T · m² E) 25 T · m²

Accepted Answer

The magnetic flux through a coil is given by the product of the magnetic field strength, the area of the coil, and the cosine of the angle between the normal to the coil and the magnetic field. In this case, the normal to the coil is in the direction of the magnetic field, so the cosine of the angle is 1. Therefore, the magnetic flux through the coil is:$$\Phi = BA\cos	heta = (0.25 	ext{ T})(10 	ext{ cm}^2)(1) = 5.0 	imes 10^{-3} 	ext{ T}\cdot	ext{m}^2$$

Question 16

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

Accepted Answer

The magnetic flux through the coil is given by Φ = Φ₀ * cos(θ), where Φ₀ is the maximum flux and θ is the angle between the normal to the coil and the magnetic field. Here, Φ₀ = 4.0 * 10⁻³ T·m² and θ = 60°. So, Φ = 4.0 * 10⁻³ * cos(60°) = 4.0 * 10⁻³ * 0.5 = 2.0 * 10⁻³ T·m².

Question 17

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 time variation 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 is proportional to the rate of change of flux through the loop. Therefore, the correct option is B, which states that the emf induced is proportional to the time variation of the magnetic flux. The other options are not correct because A is only the magnetic flux, and does not consider time variation, C is the formula for average current, and D is the formula for magnetic flux, not emf.

Question 18

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 T 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

Accepted Answer

When a conductor moves perpendicular to a magnetic field, a voltage is induced across its ends. This is known as the electromagnetic induction phenomenon. The magnitude of the induced voltage, in volts per meter, is given by the formula:

E = Bvl

where E is the electric field, B is the magnetic field, v is the velocity of the conductor, and l is the length of the conductor.

In this problem, the velocity and the magnetic field are given, and the length of the conductor is 2 meters. Therefore, we can calculate the electric field as:

E = (5.0 T) x (6.0 m/s) x (2.0 m) = 60 V/m

However, the problem asks for the magnitude of the electric field, which is given by the absolute value of E. Also, the answer should be in millivolts per meter, not volts per meter. Therefore, we have:

|E| = 60 x 10^3 mV/m = 30 mV/m

Hence, the correct choice is (C).

Question 19

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 m T 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 20

The emf produced by an ac generator is given by $\varepsilon$ = $\omega$NBA sin $\omega$t.In the SI system,what is the value of $\omega$ for a frequency of 60.0 Hz?
A) 60.0 Hz
B) 120 rad/s
C) 2.00 $\pi$ rad/s
D) 377 rad/s
E) 377 Hz

Accepted Answer

The angular frequency $\omega$ is related to the frequency $f$ by the formula $\omega = 2\pi f$. For a frequency of 60.0 Hz, $\omega = 2\pi \times 60.0 = 377$ rad/s.

Quiz 20: Electromagnetic Induction

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

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

A conducting rod is sliding on metal rails with velocity v.A magnetic field B is into the paper,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?

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 m T magnetic field is perpendicular to both the rod and its velocity.If the resistance of the rod is 15 m $\Omega$ , what is the current in the rod?

For the typical "household ac voltage" of 120 V,what is the amplitude of the emf?

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

A 20 turn coil of area 10 cm² is placed in a magnetic field so that the normal to its area is in the direction of the field.If the field originally has a value of 0.25 T that increases to 0.35 T in 2.0 s,what is the average emf induced in the coil?

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 m T magnetic field is perpendicular to both the rod and its velocity.What is the potential difference between the ends of the rod?

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?

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

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 its area is in the direction of 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 4.0 $\times$ 10^-3 T·m² through it as its area is perpendicular to a uniform magnetic field.When the coil is rotated 60 $^{\circ}$ (so that its normal makes a 60 $^{\circ}$ angle with the field) ,what is the flux through it?

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

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 T magnetic field is perpendicular to both the rod and its velocity.What is the magnitude of the electric field in 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 m T magnetic field is perpendicular to both the rod and its velocity.What is the magnetic flux swept through per second by the rod?

The emf produced by an ac generator is given by $\varepsilon$ = $\omega$ NBA sin $\omega$ t.In the SI system,what is the value of $\omega$ for a frequency of 60.0 Hz?