Q: A capacitor of capacitance $$C is $$charged to voltage $$V$$ and then connected in series with an inductor $$L. $$What is the maximum current in the circuit during oscillations?

$$I_{\text{max}} = V \sqrt{\frac{C}{L}}$$

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

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

Question 1

A square loop of wire with side length $$a is $$placed in a uniform magnetic field $$B$$ pointing out of the page. If the loop is rotated by $$90^	ext{o} in$$ $$0.2$$ seconds, what is the magnitude of the average induced emf in the loop?

Accepted Answer

$$\frac{B a^2$}{0.2}$$

Question 2

An LC circuit consists of a $$2\,\mu	ext{F}$$ capacitor and a $$0.5\,	ext{H}$$ inductor. If the initial charge on the capacitor is $$Q_0$$, what is the angular frequency of oscillation?

Accepted Answer

$$\omega = \frac{1}{\sqrt{LC}}$$

Question 3

A copper ring lies flat on a table. A bar magnet is dropped vertically through the center of the ring. What is the direction of the induced current in the ring as the magnet falls?

Accepted Answer

Counterclockwise (when viewed from above)

Question 4

Which of the following correctly expresses the energy stored in an inductor with inductance $$L$$ carrying current $$I$$?

Accepted Answer

$$U = \frac{1}{2} L I^2$

Question 5

A wire carries current $$I$$ out of the page. What is the direction of the magnetic field at a point to the right of the wire?

Accepted Answer

Downward (toward the bottom of the page)

Question 6

A solenoid of length $$l$$ and $$N$$ turns carries current $$I. $$What is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ \frac{N}{l} I$$

Question 7

A circuit contains a battery, a resistor $$R$$, and an inductor $$L in $$series. Immediately after the switch is closed, what is the current through the inductor?

Accepted Answer

Zero

Question 8

A long straight wire carries a current $$I. $$What is the expression for the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

$$B = \frac{\mu_0$ I}{2 \pi r}$$

Question 9

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

Accepted Answer

$$F = q v B$$

Question 10

A capacitor of capacitance $$C is $$charged to voltage $$V$$ and then connected in series with an inductor $$L. $$What is the maximum current in the circuit during oscillations?

Accepted Answer

$$I_{	ext{max}} = V \sqrt{\frac{C}{L}}$$

Question 11

A circular loop of radius $$r is $$placed in a time-varying magnetic field $$B(t) = B_0$ \sin(\omega t). $$What is the induced emf in the loop?

Accepted Answer

$$\mathcal{E} = \pi r^2$ B_0$ \omega \cos(\omega t)$$

Question 12

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

Accepted Answer

Such that its own field opposes the increase (Lenz's Law)

Question 13

A solenoid is connected to a battery and a switch. When the switch is opened, what happens to the current in the solenoid?

Accepted Answer

It decreases rapidly but the inductor opposes the change

Question 14

A transformer has $$N_1$$ turns on the primary coil and $$N_2$$ turns on the secondary coil. If the input voltage is $$V_1$$, what is the output voltage $$V_2$$?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$N_2$$}{$$N_1$$}$$

Question 15

A conducting rod moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the emf induced across the ends of the rod of length $$l$$?

Accepted Answer

$$\mathcal{E} = B l v$$

Question 16

A circuit contains a resistor $$R$$, inductor $$L$$, and battery $$V in $$series. What is the time constant $$	au$$ for the current to reach $$63\% of $$its final value?

Accepted Answer

$$	au = \frac{L}{R}$$

Question 17

A charged particle moves in a circle of radius $$r in a $$uniform magnetic field $$B. $$What is the expression for its speed $$v$$?

Accepted Answer

$$v = \frac{q B r}{m}$$

Question 18

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

Accepted Answer

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

Question 19

A parallel plate capacitor is connected to a battery and then disconnected. If a dielectric is inserted between the plates, what happens to the stored energy?

Accepted Answer

It decreases

Electromagnetic Induction, Magnetic Fields, and Circuits: Study Notes for Physics 10320 Exam 3

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