Q: Two parallel electrodes are separated by $$1.0\ \mathrm{mm}$$, have a width of $$1.0\ \mathrm{cm}$$, and extend $$1.0\ \mathrm{cm}$$ into the page. What is the capacitance of this system? (Assume air between the plates, $$\$$epsilon_0$$ = 8.85 \times 10$$^{-12}$$\ \mathrm{F/m})$$

$$C = 8.85 \times 10$$^{-13}$$\ \mathrm{F}$$

Q: A wire consists of straight and curved portions, carrying current $$I. At $$the center of the circular arc of radius $$R$$, what is the magnetic field due to the arc (angle $$\theta in $$radians)?

$$B = \dfrac{\mu_0$ I \theta}{4\pi R}$$

Q: In an RLC circuit, what is the phase angle $$\phi$$ between the source voltage and the current?

$$\tan\phi = \dfrac{X_L - X_C}{R}$$

Question 1

A hollow metal sphere has inner radius $$a$$ and outer radius $$b. A $$point charge $$+Q$$ sits at the center of the hollow sphere. What is the magnitude of the electric field in the region $$r \u003c a ($$inside the cavity)?

Accepted Answer

$$E = \dfrac{Q}{4\pi\$$epsilon_0$$ r^2$}$$

Question 2

For the same hollow metal sphere with a point charge $$+Q at $$the center, what is the electric field in the region $$a \u003c r \u003c b ($$inside the conducting shell)?

Accepted Answer

$$E = 0$$

Question 3

A hollow metal sphere with a point charge $$+Q at $$its center is electrically neutral overall. What is the charge induced on the inner surface of the shell?

Accepted Answer

$$-Q$$

Question 4

A hollow metal sphere with a point charge $$+Q at $$its center is electrically neutral overall. What is the charge on the outer surface of the shell?

Accepted Answer

$$+Q$$

Question 5

A thin rod of length $$L$$ has total charge $$Q$$ uniformly distributed along its length. What is the expression for the electric field at a point $$P on $$the axis of the rod, at a distance $$r$$ from the center of the rod?

Accepted Answer

$$E = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{Q}{L} \left( \dfrac{1}{r - L/2} - \dfrac{1}{r + L/2} \right)$$

Question 6

In a circuit, three capacitors are connected as follows: $$C_1 = 4$$\ \mu\mathrm{F}$$ and C_2$ = 12\ \mu\mathrm{F}$$ are in series, and their combination is in parallel with $$C_3 = 2$$\ \mu\mathrm{F}$$. What is the equivalent capacitance of the circuit?

Accepted Answer

$$C_{eq} = 5\ \mu\mathrm{F}$$

Question 7

Two parallel electrodes are separated by $$1.0\ \mathrm{mm}$$, have a width of $$1.0\ \mathrm{cm}$$, and extend $$1.0\ \mathrm{cm}$$ into the page. What is the capacitance of this system? (Assume air between the plates, $$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{F/m})$$

Accepted Answer

$$C = 8.85 	imes 10$$^{-13}$$\ \mathrm{F}$$

Question 8

In a circuit, the current through each resistor is identical. If the resistors are $$R$$ and $$R_x$$, and the batteries are identical, what must be true about $$R_x$$ for the currents to be equal?

Accepted Answer

$$R_x = R$$

Question 9

A battery with unknown internal resistance $$r is $$connected to a $$5\ \Omega$$ and a $$10\ \Omega$$ resistor in series. If the total current is $$1.5\ \mathrm{A}$$ and the current through the $$10\ \Omega$$ resistor is $$1.0\ \mathrm{A}$$, what is the emf $$\mathcal{E} of $$the battery?

Accepted Answer

$$\mathcal{E} = 20\ \mathrm{V}$$

Question 10

A wire consists of straight and curved portions, carrying current $$I. At $$the center of the circular arc of radius $$R$$, what is the magnetic field due to the arc (angle $$	heta in $$radians)?

Accepted Answer

$$B = \dfrac{\mu_0$ I 	heta}{4\pi R}$$

Question 11

A conducting bar of length $$L$$ and mass $$m$$ slides on frictionless rails in a uniform magnetic field $$B$$ with a current $$I$$ flowing through it. What is the expression for the speed $$v of $$the bar when it leaves the rails, assuming it started from rest and the only force is magnetic?

Accepted Answer

$$v = \dfrac{B^2$ L^2$ I}{m}$$

Question 12

A rectangular loop of wire ($$5.0\ \mathrm{cm}$$ wide) is pushed into a $$0.53\ \mathrm{T}$$ magnetic field at $$67\ \mathrm{m/s}. $$The loop's resistance is $$0.79\ \Omega. $$What is the magnitude of the induced current?

Accepted Answer

$$I = 0.42\ \mathrm{A}$$

Question 13

In a European RLC circuit, the source voltage is $$240\ \mathrm{V} at$$ $$50\ \mathrm{Hz}$$, $$R = 117\ \Omega$$, $$C = 9\ \mu\mathrm{F}$$, and $$L = 0.170\ \mathrm{H}. $$What is the capacitive reactance $$X_C$$?

Accepted Answer

$$X_C = 354\ \Omega$$

Question 14

For the same RLC circuit, what is the resonance frequency $$f_0$$?

Accepted Answer

$$f_0$$ = \dfrac{1}{2\pi\sqrt{LC}}$$

Question 15

In an RLC circuit, what is the phase angle $$\phi$$ between the source voltage and the current?

Accepted Answer

$$	an\phi = \dfrac{X_L - X_C}{R}$$

Question 16

A loop is pushed into a magnetic field. According to Lenz's Law, what is the direction of the induced current?

Accepted Answer

It opposes the change in magnetic flux through the loop.

Question 17

Which of the following best explains why power is transmitted at high voltage and low current over long distances?

Accepted Answer

To minimize energy loss due to resistive heating ($$P_{loss} = I^2$ R).$$

Physics 172 Final Exam Study Guide: Electric Fields, Circuits, Magnetism, and AC Circuits

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