Deck 21: Magnetic Induction

Question 1

Three loops of wire, one circular, one rectangular, and one square, are made from identical lengths of wire. If the loops are in the same increasing magnetic field perpendicular to the plane of the coils, which loop has the least induced emf?

A) the square one
B) the rectangular one
C) the circular one
D) All three would have the same emf induced.

Answer 1

the rectangular one

Question 2

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from to in 0.47 s. What is the induced emf in the wire?

A)
B)
C)
D)

Answer 2

Question 3

A uniform 1.5-T magnetic field passes perpendicularly through the plane of a wire loop 0.30 m² in area. What flux passes through the loop?

A) 0.135 T.m²
B) 5.0 T.m²
C) 0.45 T.m²
D) 0.25 T.m²

Answer 3

0.45 T.m²

Question 4

A circular loop of wire has its radius doubled in time Δt. A uniform magnetic field is at an angle of 60^° to the plane of the coil, and the magnetic field halves its intensity in the same time interval Δt. During this interval, what happens to the flux through the coil?

A) It decreases.
B) It remains the same.
C) It increases.
D) More information is needed to make this conclusion.

Question 5

The magnetic field inside a circular loop of wire of radius 30 cm increases at a constant rate from to in 0.47 s. If the resistance of the loop is 0.31 $\Omega$ , what is the current in the loop?

A)
B)
C)
D)

Question 6

A 0.200-m wire is moved parallel to a 0.500-T magnetic field at a speed of 6.00 m/s. What emf is induced across the ends of the wire?

A) 1.00 V
B) 0.600 V
C) 2.25 V
D) zero

Question 7

Electricity may be generated by rotating a loop of wire between the poles of a magnet. The induced current is least when:

A) the plane of the loop is perpendicular to the magnetic field.
B) the plane of the loop makes an angle of 45° with the magnetic field.
C) the magnetic flux through the loop is a maximum.
D) the plane of the loop is parallel to the magnetic field.

Question 8

A straight wire of length is oriented east-west and is in a magnetic field B pointing north. The wire is moving upward at a constant speed v. Which end of the rod is positively charged?

A) neither
B) the west end
C) the east end
D) both ends

Question 9

A metal rod is falling toward the surface of the Earth near the equator. As it falls, one end of the rod becomes positively charged due to the motional emf of the rod through the Earth's magnetic field. The rod is oriented so that:

A) the rod is horizontal with the positive end toward the east.
B) the rod is horizontal with the positive end toward the north.
C) the rod is vertical with the positive end higher.
D) the rod is horizontal with the positive end toward the west.

Question 10

A straight wire of length is oriented east-west and is in a magnetic field B pointing north. The wire is moving downward at a constant speed v. If the resistance of the rod is R, what is the current through the rod?

A) B^2
2 v ²/R²
B) R/B v
C) B v /R
D) not given

Question 11

A double loop of wire (making 2 turns) is in the x-y plane centered at the origin. A uniform magnetic field is increasing at a constant rate in the negative z direction. In which direction is the induced magnetic field in the loop?

A) There is no induced field because of the double loop.
B) There is no induced field because the rate of change of the magnetic field is constant.
C) in the negative z direction
D) in the positive z direction

Question 12

A coil is placed in a magnetic field and has a flux $\varPsi$ _B through it. The coil is stressed so that its area reduces to 60% of its original value. If the plane of the coil stays the same and the flux through it remains the same, how must the magnetic field change?

A) It must increase by 60%.
B) It must increase by 120%.
C) It must decrease by 40%.
D) It must increase by 67%.

Question 13

An airplane with a wingspan of 60.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.400 * l0^-4 T. If the induced potential between wingtips is 0.600 V, what is the plane's speed?

A) 338 m/s
B) 375 m/s
C) 250 m/s
D) 417 m/s

Question 14

Magnetism had been a known phenomenon for some time before its relation to electric currents was found. That a current in a wire produces a magnetic field was discovered by:

A) "Ampere."
B) "Maxwell."
C) " $\text{\o}$ rsted."
D) "Tesla."

Question 15

A loop of area 0.250 m² is in a uniform 0.0200-T magnetic field. If the flux through the loop is 3.21 * 10^-3 T·m², what angle does the normal to the plane of the loop make with the direction of the magnetic field?

A) 40.0°
B) 37.5°
C) 50.0°
D) This is not possible.

Question 16

A large jetliner with a wingspan of 40 m flies horizontally and due north at a speed of 300 m/s in a region where the magnetic field of the earth is 51 µT directed 24.1° below the horizontal. What is the magnitude of the induced emf between the ends of the wing?

A) 350 mV
B) 750 mV
C) 550 mV
D) 250 mV

Question 17

A uniform 4.5-T magnetic field passes through the plane of a wire loop 0.20 m² in area. What flux passes through the loop when the direction of the 4.5-T field is at a 30° angle to the normal of the loop plane?

A) 0.39 T.m²
B) 5.0 T.m²
C) 0.78 T.m²
D) 0.225 T.m²

Question 18

The units T·m²/s are equivalent to:

A) V.
B) N/m.
C) W.
D) webers.

Question 19

A coil in a magnetic field encloses a flux of 0.256 T·m² when the angle between the normal to the coil and the direction of the magnetic field is 70.0°. What flux would go through the coil if the angle were changed to 30.0°?

A) 0.648 T·m²
B) 0.573 T·m²
C) 0.114 T·m²
D) 0.198 T·m²

Question 20

A sensitive ammeter is connected to a wire loop and placed within the magnetic field of a strong horseshoe magnet. The ammeter shows a deflection when:

A) the wire is moved parallel to the field.
B) neither wire nor magnet is moving.
C) the wire's axis is parallel to the field.
D) the wire is moved perpendicularly to the field.

Question 21

If a bar magnet is falling through a loop of wire, the induced current in the loop of wire sets up a field which exerts a force on the magnet. This force between the magnet and the loop will be repulsive when:

A) the magnet enters the loop.
B) the magnet is leaving the loop.
C) never.
D) the magnet is halfway through.

Question 22

A coil is placed in a changing magnetic field and an emf is induced. What happens to the induced emf if the rate of change of magnetic field doubles?

A) The emf quadruples.
B) The emf increases by a factor of 16.
C) There is no change.
D) The emf doubles.

Question 23

The principle or law that says "an induced emf in a circuit loop produces a current whose magnetic field opposes further change of magnetic flux" is credited to:

A) Ampere.
B) Volta.
C) Lenz.
D) Faraday.

Question 24

A 10-turn square coil of area 0.036 m² and a 6-turn circular coil are both placed at an angle of 25° to the same changing magnetic field. The voltage induced in each of the coils is the same. What is the area of the circular coil?

A) 0.072 m²
B) 0.060 m²
C) 0.0720 m²
D) 0.60 m²

Question 25

A long wire along the x axis is carrying a current increasing at a constant rate in the +x direction. A rectangular coil lies in the x-y plane in the 4th quadrant. In which direction is the induced magnetic field at the center of the rectangular coil?

A) in the -z direction
B) There is no direction; the induced current in the coil is zero since the x axis and the coil are in the same plane.
C) in the +z direction
D) No direction can be found since the orientation of the rectangular coil is not given.

Question 26

A square coil, enclosing an area with sides 3.0 cm long, is wrapped with 2500 turns of wire. A uniform magnetic field perpendicular to its plane is turned on and increases to 0.12 T during an interval of 1.0 s. What average voltage is induced in the coil?

A) 2.5 V
B) 0.27 V
C) 1.2 V
D) 0.12 V

Question 27

By what factor is the self-inductance of a solenoid changed if only its cross-sectional area, A, is doubled?

A) 1/2
B) 4
C) 2
D) 8

Question 28

The current in a coil with a self-inductance of 1.5 mH increases from 0 to 2.0 A in a tenth of a second. What is the induced emf in the coil?

A) 15 mV
B) 0.30 V
C) 0.10 V
D) 30 mV

Question 29

A bar magnet is falling through a loop of wire with constant velocity. The north pole enters first. As the south pole leaves the loop of wire, the induced current (as viewed from above) will be:

A) along the length of the magnet.
B) zero.
C) counterclockwise.
D) clockwise.

Question 30

A bar magnet is falling through a loop of wire with constant velocity. The south pole enters first. As the magnet leaves the wire, the induced current (as viewed from above):

A) is along the length of the magnet.
B) is clockwise.
C) is counterclockwise.
D) is zero.

Question 31

According to Lenz's law the direction of an induced current in a conductor will be that which tends to produce which of the following effects?

A) oppose the effect which produces it
B) enhance the effect which produces it
C) produce the greatest voltage
D) produce a greater heating effect

Question 32

A planar loop consisting of four turns of wire, each of which encloses 250 cm², is oriented perpendicularly to a magnetic field that increases uniformly in magnitude from 10 mT to 25 mT in a time of 5.0 ms. What is the resulting induced current in the coil if the resistance of the coil is 5.0 $\Omega$ ?

A) 48 mA
B) 0.24 mA
C) 12 mA
D) 60 mA

Question 33

A flat coil of wire consisting of 20 turns, each with an area of 80 cm², is positioned perpendicularly to a uniform magnetic field that increases its magnitude at a constant rate from 2.0 T to 6.0 T in 2.0 s. If the coil has a total resistance of 0.40 $\Omega$ , what is the magnitude of the induced current?

A) 500 mA
B) 70 mA
C) 140 mA
D) 800 mA

Question 34

What is the self-inductance in a coil that experiences a 3.0-V induced emf when the current is changing at a rate of 37 A/s?

A) 81 mH
B) 37 mH
C) 27 mH
D) 45 mH

Question 35

A bar magnet is falling through a loop of wire with constant velocity. The south pole enters first. The induced current will be greatest in magnitude when the magnet is located so that:

A) with no acceleration, the induced current is zero.
B) the loop is near the south pole only.
C) the loop is near either the north or the south pole.
D) the loop is near the middle of the magnet.

Question 36

Two loops of wire are arranged so that a changing current in one will induce a current in the other. If the current in the first is increasing counterclockwise by 1.0 A every second, the induced current in the second loop will:

A) be increasing counterclockwise.
B) increase clockwise also.
C) stay zero.
D) stay constant.

Question 37

If the induced current in a wire loop were such that the flux it produces is in the same direction as the change in external flux causing the current, which of the following conservation laws would end up being violated?

A) energy
B) charge
C) momentum
D) angular momentum

Question 38

A coil with a self-inductance of 0.75 mH experiences a constant current buildup from zero to 15 A in 0.25 s. What is the induced emf during this interval?

A) 0.045 V
B) 0.47 V
C) 0.030 V
D) 0.019 V

Question 39

By what factor is the self-inductance of a solenoid changed if only its number of coil turns, N, is doubled?

A) 8
B) 1/2
C) 4
D) 2

Question 40

The self-inductance of a solenoid increases under which of the following conditions?

A) Only the cross sectional area is decreased.
B) Only the number of coils per unit length is decreased.
C) Only the number of coils is increased.
D) Only the solenoid length is increased.

Question 41

An inductor, battery, resistor, ammeter, and switch are connected in series. If the switch, initially open, is now closed, what is the current's final value?

A) zero
B) battery voltage divided by resistance
C) battery voltage times inductance
D) battery voltage divided by inductance

Question 42

An RL series circuit has the following components: 5.0-mH coil, 4.8- $\Omega$ resistor, 12-V battery, ammeter, and switch. After the switch is closed for a long time, find the final value of the current.

A) 12 A
B) 2400 A
C) 2.5 A
D) 58 A

Question 43

An inductor has 1000 turns/m and an internal volume of 30 cm³. What is its inductance?

A) 0.38 H
B) 38 $\mu$ H
C) 3.8 $\mu$ H
D) Insufficient information is given.

Question 44

A series circuit contains a 12-V battery, a 4.0- $\Omega$ resistor, and a 12-mH inductor. If the switch to the battery is closed at t = 0, find the time required for the current in the circuit to reach 63% of its final value.

A) 1.5 ms
B) 3.0 ms
C) 4.0 ms
D) 5.0 ms

Question 45

In a circuit made up of inductor L, resistor R, ammeter, battery, and switch in series, the current is greatest at which of the following times, as measured after the switch is closed?

A) ten time constants
B) at a time t = L/R
C) one time constant
D) zero

Question 46

One time constant after an RL circuit has its switch closed, how does the current I in it compare to the maximum current I_max that occurs for this circuit?

A) I > I_max/2
B) I = I_max/2
C) I < I_max/2
D) Without knowing R and L, this cannot be determined.

Question 47

What is the stored energy in a 1.5-mH coil carrying a current of 4.0 A?

A) 12 *10^-3 J
B) 4.0 *10^-3 J
C) 8.0 *10^-3 J
D) 2.0 *10^-3 J

Question 48

By what factor is the self-inductance of a solenoid changed if its length is doubled and its number of coil turns is tripled?

A) 2/9
B) 9/2
C) 3/4
D) 4/3

Question 49

A circuit consists of a 10-mH coil, a 12- $\Omega$ resistor, a 60- $\Omega$ resistor, a 9.0-V battery, and a switch, all in series. What is the time constant of this circuit?

A) 2.5 * 10^-3 s
B) 5.6 *10^-4 s
C) 1.4 * 10^-4 s
D) 9.0 * 10^-2 s

Question 50

Which of the following is referred to as mutual inductance?

A) Two unconnected inductors have their coils wound in the same pattern.
B) Two solenoids have the same inductance.
C) The changing flux from one inductor produces an emf in another inductor.
D) The numerical value of one inductance is the reciprocal of another inductance in the same circuit.

Question 51

In a circuit made up of inductor, resistor, ammeter, battery, and switch in series, at which of the following times after the switch is closed is the rate of current increase greatest?

A) reciprocal of one time constant
B) zero
C) ten time constants
D) one time constant

Question 52

Two solenoids, wound from wire from the same spool, have the same length and cross-sectional area, but solenoid #1 has twice the turns of solenoid #2. If these solenoids are each connected to a circuit, and the only non-negligible resistance is that of the solenoids, which solenoid gives the greater time constant and by what factor?

A) #2 by a factor of 2
B) #2 by a factor of 4
C) #1 by a factor of 2
D) No answer above is completely correct.

Question 53

An RL series circuit has the following components: 6.0-mH coil, 0.50- $\Omega$ resistor, 12-V battery, ammeter, and switch. What is the time constant of this circuit?

A) 2.5 *10^-2 s
B) 12 *10^-3 s
C) 200 s
D) 5.0 *10^-3 s

Question 54

The magnetic field going through a stationary circular loop increases from zero to 5 T in a certain time t. The induced current in the loop will depend on the radius of the loop, r, the resistance of the loop, R, and the time, t. If two of these stay constant, the induced current can be directly proportional to:

A) r.
B) t.
C) R.
D) none of these

Question 55

A 12-V battery is connected in series with a switch, resistor, and coil. If the circuit's time constant is 2.0 *10^-4 s and the final steady current after the switch is closed becomes 2.0 A, what is the value of the inductance?

A) 2.4 mH
B) 48 mH
C) 9.6 mH
D) 1.2 mH

Question 56

A circuit consists of a 10-mH coil, a 9.0-V battery, a parallel combination of a 48- $\Omega$ resistor and a 24- $\Omega$ resistor, and a switch, all in series. What is the time constant of this circuit?

A) 1.2 * 10^-3 s
B) 6.3 *10^-4 s
C) 9.0 *10^-2 s
D) This circuit has 2 time constants.

Question 57

In an RL circuit with time constant 3.0 s, what does the time constant become if the resistance is doubled and the inductance is tripled?,

A) 2.0 s
B) 18 s
C) 9.0 s
D) 4.5 s

Question 58

The unit of inductance, the henry, is equivalent to:

A) J/C.
B) V/m.
C) V·s/A.
D) none of the units given.

Question 59

An emf of 0.26 V is induced in a 0.40-H inductor. What is the rate of change of current through the inductor?

A) 0.80 A/s
B) 1.3 A/s
C) 0.13 A/s
D) 0.65 A/s

Question 60

The first solenoid has 2 times the diameter, 2 times the number of turns, and 2 times the length of the second solenoid. Which solenoid has the greater inductance and by what factor?

A) the first solenoid by a factor of 8
B) the second solenoid by a factor of 8
C) the first solenoid by a factor of 16
D) the second solenoid by a factor of 32

Question 61

By what factor does the maximum energy stored in a series RL circuit change if the resistance is doubled and the inductance is tripled in the circuit?

A) 0.67
B) 0.75
C) 0.50
D) 1.5

Question 62

A 12-V battery is connected in series with a switch, 6.0- $\Omega$ resistor, and coil. What energy is stored in the coil when the current is 2.0 A? The time constant is 2.0 *10^-3 s.

A) 9.6 *10^-3 J
B) 4.8 *10^-3 J
C) 2.9 *10^-2 J
D) 2.4 *10^-2 J

Question 63

The function of the electric motor is which one of the following conversion processes?

A) mechanical energy to electrical
B) alternating current to direct
C) low voltage to high or vice versa
D) electrical energy to mechanical

Question 64

The basic function of the electric generator is which of the following conversion processes?

A) alternating current to direct
B) electrical energy to mechanical
C) low voltage to high or vice versa
D) mechanical energy to electrical

Question 65

A changing current in one loop of wire can induce a current in another loop of wire even though the wires do not touch. The induced current appears almost instantaneously for loops close together. How can this energy exchange happen?

A) This is one of those things for which science has no adequate explanation yet.
B) The second loop is affected by the thermal exchange from the heating of the first loop.
C) It is a gravitational effect on the electrons.
D) It is done via an electromagnetic wave.

Question 66

Superconductors have been discussed as a means for electrical energy storage. Because they are resistanceless, a current once started in a loop would continue without loss. If a current of 1.0 * 10⁴ A were started in a huge toroidal coil of radius 1.0 km and inductance 70 H, how much electrical energy (in kWh) could be stored?

A) 480 kWh
B) 300 kWh
C) 690 kWh
D) 970 kWh

Question 67

The operation of an electric motor depends on which of the following effects?

A) the force acting on a current-carrying wire in a magnetic field
B) the Doppler effect
C) current from the motion of a wire in a magnetic field
D) the photoelectric effect

Question 68

How is the energy stored in a current-carrying inductor related to its self-inductance, L?

A) directly proportional to L^1/2
B) directly proportional to L
C) inversely proportional to L
D) directly proportional to L²

Question 69

"GFI" stands for:

A) grand flux indicator.
B) gauss-free invention.
C) ground forcing indicator.
D) ground fault interrupter.

Question 70

How is the energy stored in a current-carrying inductor related to the current value, I?

A) directly proportional to I^1/2
B) directly proportional to I²
C) inversely proportional to I
D) directly proportional to I