Question 1

A conducting loop of resistance $$R$$ and side length $$l is $$pulled with constant speed $$v$$ into a region with a uniform magnetic field $$B$$ perpendicular to the plane of the loop. What is the induced emf in the loop when it is partially inside the field?

Accepted Answer

$$Blv$$

Question 2

A square conducting loop is pulled out of a uniform magnetic field at constant speed. Which of the following best describes the direction of the induced current as the loop exits the field?

Accepted Answer

Clockwise, to oppose the decrease in magnetic flux

Question 3

Given two coaxial solenoids with $$N_1$$ and $$N_2$$ turns, length $$l$$, and cross-sectional area $$A$$, what is the mutual inductance $$M$$ between them?

Accepted Answer

$$M = \mu_0$ N_1$ N_2$ A / l$$

Question 4

A bar of mass $$m$$ slides on frictionless conducting rails in a uniform magnetic field $$B$$ with resistance $$R. If $$the bar moves at speed $$v$$, what is the induced emf?

Accepted Answer

$$\epsilon = Blv$$

Question 5

For the same bar described above, what is the magnetic force acting on the bar when it is moving at speed $$v$$?

Accepted Answer

$$F = \frac{B^2$ l^2$ v}{R}$$

Question 6

A bar is sliding at terminal speed $$v_{ter} in a $$uniform magnetic field. What is the expression for $$v_{ter}$$?

Accepted Answer

$$v_{ter} = \frac{F_{app} R}{B^2$ l^2$}$$

Question 7

If the acceleration of the bar is $$a = \frac{F_{app} - \frac{B^2$ l^2$ v}{R}}{m}$$, what happens to the acceleration as $$v$$ approaches $$v_{ter}$$?

Accepted Answer

It approaches zero

Question 8

In a circuit with two branches, one with a larger inductance $$L$$, which branch will reach its maximum current first after the switch is closed?

Accepted Answer

The branch with smaller $$L$$

Question 9

A graph shows the current in two branches of a circuit with different inductances reaching their maximum at the same time. What is wrong with this graph?

Accepted Answer

It ignores the time constant difference due to inductance

Question 10

A conducting bar moves in a uniform magnetic field. If the resistance of the circuit is doubled, what happens to the terminal speed $$v_{ter}$$?

Accepted Answer

It doubles

Question 11

Which of the following best describes the relationship between the rate of change of magnetic flux and the induced emf in a loop?

Accepted Answer

$$\epsilon = -\frac{d\Phi_B}{dt}$$

Question 12

A square loop is pulled at constant speed out of a magnetic field. What happens to the induced current as the loop completely exits the field?

Accepted Answer

It drops to zero

Question 13

If the applied force on a sliding bar in a magnetic field is suddenly removed, what happens to the bar's velocity?

Accepted Answer

It decreases exponentially

Question 14

A coil with $$N$$ turns and area $$A is $$placed in a time-varying magnetic field $$B(t). $$What is the induced emf in the coil?

Accepted Answer

$$\epsilon = -N A \frac{dB}{dt}$$

Question 15

A bar of mass $$m$$ slides on frictionless rails in a uniform magnetic field $$B$$ with resistance $$R. If $$the bar starts from rest and a constant force $$F_{app} is $$applied, what is the equation for its velocity as a function of time?

Accepted Answer

$$v(t) = v_{ter} (1 - e$$^{-\frac{B^2 l^2}$${mR} t})$$

Study Notes: Electromagnetic Induction and Inductance (Chapters 29 & 30)

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