Question 1

A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of 2.0 A the magnetic flux through each turn is:

Accepted Answer

A)  0 
B)  3.5 *10-4 wb 
C)  7.0 *10-4 wb 
D)  7.0 *10-3 wb 
E)  7.0 * 10-2 wb 
A)  0 
B)  3.5 *10-4 wb 
C)  7.0 *10-4 wb 
D)  7.0 *10-3 wb 
E)  7.0 * 10-2 wb C

Question 2

An inductance L, resistance R, and ideal battery of emf $\varepsilon$ are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the emf of the inductor is given by:

Accepted Answer

A)  $\varepsilon$(1 - e-Lt/R) 
B)  $\varepsilon$e-Lt/R 
C)  $\varepsilon$(1 + e-Rt/L) 
D)  $\varepsilon$e-Rt/L 
E)  $\varepsilon$(1 - e-Rt/L) 
A)  $\varepsilon$(1 - e-Lt/R) 
B)  $\varepsilon$e-Lt/R 
C)  $\varepsilon$(1 + e-Rt/L) 
D)  $\varepsilon$e-Rt/L 
E)  $\varepsilon$(1 - e-Rt/L) D

Question 3

A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is:

Accepted Answer

A)  rotated about a north-south axis 
B)  rotated about an east-west axis 
C)  moved rapidly, without rotation, toward the east 
D)  moved rapidly, without rotation, toward the south 
E)  moved rapidly, without rotation, toward the northwest 
A)  rotated about a north-south axis 
B)  rotated about an east-west axis 
C)  moved rapidly, without rotation, toward the east 
D)  moved rapidly, without rotation, toward the south 
E)  moved rapidly, without rotation, toward the northwest B

Question 4

As a loop of wire with a resistance of 10 $\Omega$ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:

Accepted Answer

A)  is 0 
B)  is 0.2 V 
C)  is 0.28 V 
D)  is 2 V 
E)  cannot be calculated from the given data 
A)  is 0 
B)  is 0.2 V 
C)  is 0.28 V 
D)  is 2 V 
E)  cannot be calculated from the given data

Question 5

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is:

Accepted Answer

A)  zero 
B)  clockwise 
C)  counterclockwise 
D)  depends on i1 - i2 
E)  depends on i1 + i2 
A)  zero 
B)  clockwise 
C)  counterclockwise 
D)  depends on i1 - i2 
E)  depends on i1 + i2

Question 6

An inductor with inductance L and an inductor with inductance 2L connected in parallel. When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:

Accepted Answer

A)  400 A/s 
B)  1200 A/s 
C)  1600 A/s 
D)  2000 A/s 
E)  2400 A/s 
A)  400 A/s 
B)  1200 A/s 
C)  1600 A/s 
D)  2000 A/s 
E)  2400 A/s

Question 7

A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, the emf of the larger inductor is:

Accepted Answer

A)  7.0 V 
B)  9.0 V 
C)  2.3 V 
D)  28 V 
E)  36 V 
A)  7.0 V 
B)  9.0 V 
C)  2.3 V 
D)  28 V 
E)  36 V

Question 8

A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the electric field induced at a point 2R from the cylinder axis is:

Accepted Answer

A)  zero 
B)  2R dB /dt 
C)  R dB /dt 
D)  (R/2) dB /dt 
E)  (R/4) dB /dt 
A)  zero 
B)  2R dB /dt 
C)  R dB /dt 
D)  (R/2) dB /dt 
E)  (R/4) dB /dt

Question 9

An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time 0, at which time the current is zero. The energy stored in the inductor is a maximum:

Accepted Answer

A)  just after the switch is closed 
B)  at the time t = L/R after the switch is closed 
C)  at the time t = L/R2 after the switch is closed 
D)  at the time t = 2L/R after the switch is closed 
E)  a long time after the switch is closed 
A)  just after the switch is closed 
B)  at the time t = L/R after the switch is closed 
C)  at the time t = L/R2 after the switch is closed 
D)  at the time t = 2L/R after the switch is closed 
E)  a long time after the switch is closed

Question 10

An inductance L, resistance R, and ideal battery of emf   are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the potential difference across the resistor is given by:

Accepted Answer

A)  $\varepsilon$(1 - e-Lt/R) 
B)  $\varepsilon$e-Lt/R 
C)  $\varepsilon$(1 + e-Rt/L) 
D)  $\varepsilon$e-Rt/L 
E)  $\varepsilon$(1 - e-Rt/L) 
A)  $\varepsilon$(1 - e-Lt/R) 
B)  $\varepsilon$e-Lt/R 
C)  $\varepsilon$(1 + e-Rt/L) 
D)  $\varepsilon$e-Rt/L 
E)  $\varepsilon$(1 - e-Rt/L)

Question 11

If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:

Accepted Answer

A)  twice the old 
B)  four times the old 
C)  half the old 
D)  one-fourth the old 
E)  unchanged 
A)  twice the old 
B)  four times the old 
C)  half the old 
D)  one-fourth the old 
E)  unchanged

Question 12

A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 * 10-5 T. The emf around the rim is:

Accepted Answer

A)  0 
B)  0.5 mV 
C)  3.1 mV 
D)  15 mV 
E)  30 mV 
A)  0 
B)  0.5 mV 
C)  3.1 mV 
D)  15 mV 
E)  30 mV

Question 13

The emf that appears in Faraday's law is:

Accepted Answer

A)  around a conducting circuit 
B)  around the boundary of the surface used to compute the magnetic flux 
C)  throughout the surface used to compute the magnetic flux 
D)  perpendicular to the surface used to compute the magnetic flux 
E)  none of the above 
A)  around a conducting circuit 
B)  around the boundary of the surface used to compute the magnetic flux 
C)  throughout the surface used to compute the magnetic flux 
D)  perpendicular to the surface used to compute the magnetic flux 
E)  none of the above

Question 14

Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. With S now closed, to make the pointer of G deflect toward the right one could:

Accepted Answer

A)  move the slide of the rheostat R quickly to the right 
B)  move coil P toward coil Q 
C)  move coil Q toward coil P 
D)  open S 
E)  do none of the above 
A)  move the slide of the rheostat R quickly to the right 
B)  move coil P toward coil Q 
C)  move coil Q toward coil P 
D)  open S 
E)  do none of the above

Question 15

The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field in region A should be in what direction?

Accepted Answer

A)  Right 
B)  Left 
C)  Into the page 
D)  Out of the page 
E)  Impossible, cannot be done with a constant magnetic field 
A)  Right 
B)  Left 
C)  Into the page 
D)  Out of the page 
E)  Impossible, cannot be done with a constant magnetic field

Question 16

A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to the axis of rotation. Looking in the direction of the field at the loop the induced current is:

Accepted Answer

A)  always clockwise 
B)  always counterclockwise 
C)  clockwise in the lower half of the loop and counterclockwise in the upper half 
D)  clockwise in the upper half of the loop and counterclockwise in the lower half 
E)  sometimes clockwise and sometimes counterclockwise 
A)  always clockwise 
B)  always counterclockwise 
C)  clockwise in the lower half of the loop and counterclockwise in the upper half 
D)  clockwise in the upper half of the loop and counterclockwise in the lower half 
E)  sometimes clockwise and sometimes counterclockwise

Question 17

An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time 0, at which time the current is zero. The rate of increase of the energy stored in the inductor is a maximum:

Accepted Answer

A)  just after the switch is closed 
B)  at the time t = L/R after the switch is closed 
C)  at the time t = 2L/R after the switch is closed 
D)  at the time t = (L/R)ln 2 after the switch is closed 
E)  a long time after the switch is closed 
A)  just after the switch is closed 
B)  at the time t = L/R after the switch is closed 
C)  at the time t = 2L/R after the switch is closed 
D)  at the time t = (L/R)ln 2 after the switch is closed 
E)  a long time after the switch is closed

Question 18

The normal to a certain 1-m2 area makes an angle of 60$\degree$ with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

Accepted Answer

A)  0.866 m2 
B)  1.15 m2 
C)  0.5 m2 
D)  2 m2 
E)  1 m2 
A)  0.866 m2 
B)  1.15 m2 
C)  0.5 m2 
D)  2 m2 
E)  1 m2

Question 19

A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is changed to 5 A in the opposite direction, the stored energy changes by:

Accepted Answer

A)  20 J 
B)  30 J 
C)  40 J 
D)  50 J 
E)  60 J 
A)  20 J 
B)  30 J 
C)  40 J 
D)  50 J 
E)  60 J

Question 20

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:

Accepted Answer

A)  2.0 * 103 A/s 
B)  3.6 * 103 A/s 
C)  4.6 * 103 A/s 
D)  7.0 * 103 A/s 
E)  8.1 *103 A/s 
A)  2.0 * 103 A/s 
B)  3.6 * 103 A/s 
C)  4.6 * 103 A/s 
D)  7.0 * 103 A/s 
E)  8.1 *103 A/s

Exam 30: Induction and Inductance

A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of 2.0 A the magnetic flux through each turn is:

An inductance L, resistance R, and ideal battery of emf ε\varepsilonε are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the emf of the inductor is given by:

A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is:

As a loop of wire with a resistance of 10 Ω\OmegaΩ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is:

An inductor with inductance L and an inductor with inductance 2L connected in parallel. When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is:

A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, the emf of the larger inductor is:

A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the electric field induced at a point 2R from the cylinder axis is:

An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time 0, at which time the current is zero. The energy stored in the inductor is a maximum:

An inductance L, resistance R, and ideal battery of emf are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the potential difference across the resistor is given by:

If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be:

A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 * 10-5 T. The emf around the rim is:

The emf that appears in Faraday's law is:

Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. With S now closed, to make the pointer of G deflect toward the right one could:

The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field in region A should be in what direction?

A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to the axis of rotation. Looking in the direction of the field at the loop the induced current is:

An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time 0, at which time the current is zero. The rate of increase of the energy stored in the inductor is a maximum:

The normal to a certain 1-m2 area makes an angle of 60 °\degree° with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is:

A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is changed to 5 A in the opposite direction, the stored energy changes by:

A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is:

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An inductance L, resistance R, and ideal battery of emf $\varepsilon$ are wired in series. A switch in the circuit is closed at time 0, at which time the current is zero. At any later time t the emf of the inductor is given by:

As a loop of wire with a resistance of 10 $\Omega$ moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:

A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i₁ and i₂ as indicated. If i₁ is increasing and i₂ is constant, then the induced current in the loop is:

A merry-go-round has an area of 300 m² and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 * 10^-⁵ T. The emf around the rim is:

The normal to a certain 1-m² area makes an angle of 60 $\degree$ with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is: