Q: A long solenoid with $$n = 1000\ \mathrm{turns/m}$$ carries a current of $$I = 2\ \mathrm{A}. $$What is the magnitude of the magnetic field inside the solenoid?

$$B = \mu_0$ n I = 2.51 \times 10$$^{-3}$$\ \mathrm{T}$$

Q: A coil with $$N$$ turns and area $$A is $$rotated in a uniform magnetic field $$B at $$angular frequency $$\omega. $$What is the maximum emf induced in the coil?

$$\mathcal{E}_{\text{max}} = N B A \omega$$

Question 1

A transformer has a primary coil with 100 turns and a secondary coil with 500 turns. If the primary coil is connected to a 120 V AC source, what is the output voltage across the secondary coil, assuming an ideal transformer?

Accepted Answer

$$V_s = 600\ \mathrm{V}$$

Question 2

A long solenoid with $$n = 1000\ \mathrm{turns/m}$$ carries a current of $$I = 2\ \mathrm{A}. $$What is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I = 2.51 	imes 10$$^{-3}$$\ \mathrm{T}$$

Question 3

A circuit consists of a $$12\ \mathrm{V}$$ battery, a $$6\ \Omega$$ resistor, and a $$0.5\ \mathrm{H}$$ inductor in series. Immediately after the switch is closed, what is the current through the resistor?

Accepted Answer

$$I = 0\ \mathrm{A}$$

Question 4

A point charge $$+Q is $$placed at the center of a conducting spherical shell that is initially uncharged. What is the net charge on the inner surface of the shell?

Accepted Answer

$$-Q$$

Question 5

An electromagnetic wave is propagating in the $$+y$$ direction. If the electric field points in the $$+z$$ direction, in which direction does the magnetic field point?

Accepted Answer

$$+x$$

Question 6

A toroidal coil has $$N$$ turns, carries a current $$I$$, and has a mean radius $$r. $$What is the expression for the magnetic field inside the toroid?

Accepted Answer

$$B = \dfrac{\mu_0$ N I}{2\pi r}$$

Question 7

A laser beam with power $$P = 10\ \mathrm{W} is $$directed at a perfectly reflecting surface. What is the magnitude of the radiation pressure exerted on the surface?

Accepted Answer

$$p = \dfrac{2P}{cA}$$

Question 8

A parallel-plate capacitor is connected to a battery and fully charged. If the plates are then pulled apart to double their separation while still connected to the battery, what happens to the energy stored in the capacitor?

Accepted Answer

It decreases by half

Question 9

A spaceship travels at $$0.8c$$ relative to Earth. If the trip to Alpha Centauri is $$4.3$$ light-years as measured from Earth, how much time does the trip take according to passengers on the spaceship?

Accepted Answer

$$t = 2.58\ \mathrm{years}$$

Question 10

Three parallel wires carry equal currents $$I as $$shown: $$I_1 is $$out of the page, $$I_2 is $$into the page, and $$I_3 is $$out of the page. What is the direction of the force on wire $$I_2$$ due to the other two wires?

Accepted Answer

To the left

Question 11

A conducting loop of wire is placed in a region where the magnetic field is increasing into the page. What is the direction of the induced current in the loop?

Accepted Answer

Counterclockwise

Question 12

A $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor are connected in parallel across a $$30\ \mathrm{V}$$ battery. What is the total current supplied by the battery?

Accepted Answer

$$I = 4.5\ \mathrm{A}$$

Question 13

A charged particle moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the path of the particle?

Accepted Answer

A circle

Question 14

A capacitor of $$2\ \mu\mathrm{F} is $$charged to $$12\ \mathrm{V}$$ and then disconnected from the battery. If the plates are then moved to half their original separation, what is the new voltage across the capacitor?

Accepted Answer

$$24\ \mathrm{V}$$

Question 15

A coil with $$N$$ turns and area $$A is $$rotated in a uniform magnetic field $$B at $$angular frequency $$\omega. $$What is the maximum emf induced in the coil?

Accepted Answer

$$\mathcal{E}_{	ext{max}} = N B A \omega$$

Question 16

A $$100\ \Omega$$ resistor is connected in series with a $$0.1\ \mathrm{H}$$ inductor and a $$10\ \mathrm{V}$$ battery. What is the time constant $$	au of $$the circuit?

Accepted Answer

$$	au = 0.1\ \mathrm{s}$$

Question 17

A spaceship is powered by a laser beam from Earth. If the laser has a power of $$1\ \mathrm{GW}$$ and the sail has an area of $$100\ \mathrm{m}^2$$, what is the force exerted on the sail if it is perfectly reflecting?

Accepted Answer

$$F = \dfrac{2P}{c}$$

Question 18

A uniform electric field $$E$$ points in the $$+x$$ direction. A proton is released from rest at the origin. What is the direction of its acceleration?

Accepted Answer

In the $$+x$$ direction

Question 19

A $$5\ \mu\mathrm{F}$$ capacitor is charged to $$10\ \mathrm{V}$$ and then connected across a $$10\ \Omega$$ resistor. How much time will it take for the voltage across the capacitor to drop to $$1\ \mathrm{V}$$?

Accepted Answer

$$t = 0.115\ \mathrm{s}$$

Physics 1020 Final Exam Study Guide: Electromagnetism, Circuits, and Special Relativity

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