Q: A proton is released from rest in a uniform electric field of strength $$E = 2.0 \times 10^4$\ \mathrm{N/C}$$, directed horizontally. If the proton moves a distance $$d = 0.50\ \mathrm{m} in $$the direction of the field, what is the change in its electric potential energy?

$$\Delta U_E = -qEd = -(1.6 \times 10$$^{-19}$$\ \mathrm{C})(2.0 \times 10^4$\ \mathrm{N/C})(0.50\ \mathrm{m}) = -1.6 \times 10$$^{-15}$$\ \mathrm{J}$$

Q: A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$100\ \mathrm{V}. $$How much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(2.0 \times 10$$^{-6}$$\ \mathrm{F})(100^2$\ \mathrm{V}^2) = 0.01\ \mathrm{J}$$

Q: A $$10\ \mu\mathrm{F}$$ capacitor is connected to a $$12\ \mathrm{V}$$ battery. How much charge is stored on the capacitor?

$$Q = CV = (10 \times 10$$^{-6}$$\ \mathrm{F})(12\ \mathrm{V}) = 1.2 \times 10$$^{-4}$$\ \mathrm{C}$$

Q: A metal sphere of radius $$0.10\ \mathrm{m} is $$charged to a potential of $$3.0 \times 10^5$\ \mathrm{V}. $$What is the charge on the sphere? ($$k = 9.0 \times 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$)

$$Q = \frac{Vr}{k} = \frac{3.0 \times 10^5$\ \mathrm{V} \times 0.10\ \mathrm{m}}{9.0 \times 10^9$\ \mathrm{N\cdot m^2$/C^2$$}} = 3.3 \times $$10^{-6}$$\ \mathrm{C}$

Q: A $$150\ \mu\mathrm{F}$$ camera flash capacitor is charged to $$200\ \mathrm{V}. $$How much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(150 \times 10$$^{-6}$$\ \mathrm{F})(200^2$\ \mathrm{V}^2) = 3.0\ \mathrm{J}$$

Question 1

A proton is released from rest in a uniform electric field of strength $$E = 2.0 	imes 10^4$\ \mathrm{N/C}$$, directed horizontally. If the proton moves a distance $$d = 0.50\ \mathrm{m} in $$the direction of the field, what is the change in its electric potential energy?

Accepted Answer

$$\Delta U_E = -qEd = -(1.6 	imes 10$$^{-19}$$\ \mathrm{C})(2.0 	imes 10^4$\ \mathrm{N/C})(0.50\ \mathrm{m}) = -1.6 	imes 10$$^{-15}$$\ \mathrm{J}$$

Question 2

Which of the following best describes the relationship between electric field $$E$$ and electric potential $$V in a $$uniform field?

Accepted Answer

$$E = -\frac{dV}{dx}$$

Question 3

A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$100\ \mathrm{V}. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(2.0 	imes 10$$^{-6}$$\ \mathrm{F})(100^2$\ \mathrm{V}^2) = 0.01\ \mathrm{J}$$

Question 4

What is the electric potential at a distance $$r$$ from a point charge $$Q$$?

Accepted Answer

$$V = \frac{kQ}{r}$$

Question 5

Two parallel plates are separated by $$0.01\ \mathrm{m}$$ and connected to a $$100\ \mathrm{V}$$ battery. What is the magnitude of the electric field between the plates?

Accepted Answer

$$E = \frac{V}{d} = \frac{100\ \mathrm{V}}{0.01\ \mathrm{m}} = 1.0 	imes 10^4$\ \mathrm{V/m}$$

Question 6

A $$10\ \mu\mathrm{F}$$ capacitor is connected to a $$12\ \mathrm{V}$$ battery. How much charge is stored on the capacitor?

Accepted Answer

$$Q = CV = (10 	imes 10$$^{-6}$$\ \mathrm{F})(12\ \mathrm{V}) = 1.2 	imes 10$$^{-4}$$\ \mathrm{C}$$

Question 7

Which of the following statements about equipotential lines is correct?

Accepted Answer

Equipotential lines are always perpendicular to electric field lines.

Question 8

A metal sphere of radius $$0.10\ \mathrm{m} is $$charged to a potential of $$3.0 	imes 10^5$\ \mathrm{V}. $$What is the charge on the sphere? ($$k = 9.0 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$)

Accepted Answer

$$Q = \frac{Vr}{k} = \frac{3.0 	imes 10^5$\ \mathrm{V} 	imes 0.10\ \mathrm{m}}{9.0 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}} = 3.3 	imes $$10^{-6}$$\ \mathrm{C}$

Question 9

If a dielectric with dielectric constant $$K is $$inserted between the plates of a parallel plate capacitor (while disconnected from a battery), what happens to the voltage across the plates?

Accepted Answer

The voltage decreases by a factor of $$K.$$

Question 10

Which of the following best explains why inserting a dielectric between the plates of a capacitor increases its capacitance?

Accepted Answer

The dielectric reduces the effective electric field, allowing more charge to be stored for the same voltage.

Question 11

A $$150\ \mu\mathrm{F}$$ camera flash capacitor is charged to $$200\ \mathrm{V}. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(150 	imes 10$$^{-6}$$\ \mathrm{F})(200^2$\ \mathrm{V}^2) = 3.0\ \mathrm{J}$$

Question 12

What is the energy density $$u$$ stored in the electric field between the plates of a parallel plate capacitor with electric field $$E$$ and permittivity $$\varepsilon$$?

Accepted Answer

$$u = \frac{1}{2}\varepsilon E^2$

Question 13

A $$6.5\ \mathrm{nF}$$ capacitor is connected to a $$12\ \mathrm{V}$$ battery. What is the charge stored on the capacitor?

Accepted Answer

$$Q = CV = (6.5 	imes 10$$^{-9}$$\ \mathrm{F})(12\ \mathrm{V}) = 7.8 	imes 10$$^{-8}$$\ \mathrm{C}$$

Question 14

Which of the following is a correct unit equivalence for the electric field?

Accepted Answer

$$1\ \mathrm{V/m} = 1\ \mathrm{N/C}$$

Question 15

A parallel plate capacitor has plates of area $$A = 0.02\ \mathrm{m}^2$$ separated by $$d = 1.0 	imes 10$$^{-3}$$\ \mathrm{m}$$, filled with a dielectric of $$K = 5. $$What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{C^2$/N\cdot m^2$})$$

Accepted Answer

$$C = K\$$varepsilon_0$$ \frac{A}{d} = 5 	imes 8.85 	imes 10$$^{-12}$$ \frac{0.02}{1.0 	imes 10$$^{-3}$$} = 8.85 	imes 10$$^{-10}$$\ \mathrm{F}$$

Question 16

Which of the following best describes the energy required to bring two positive point charges $$Q_1$$ and $$Q_2$$ from infinity to a separation $$r$$?

Accepted Answer

$$U = \frac{kQ_1Q_2}{r}$$

Question 17

A hydrogen atom has an electron at a distance $$r = 0.53 	imes 10$$^{-10}$$\ \mathrm{m}$$ from the proton. Estimate the work required to remove the electron from the atom (ionization energy), using $$q = -1.6 	imes 10$$^{-19}$$\ \mathrm{C}$$ and $$k = 9.0 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$.

Accepted Answer

$$W = -q \left( \frac{kQ}{r} ight ) = 1.6 	imes 10$$^{-19}$$ 	imes \frac{9.0 	imes 10^9$ 	imes 1.6 	imes 10$$^{-19}$$}{0.53 	imes 10$$^{-10}$$} = 4.3 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 18

Which of the following is NOT a typical application of capacitors?

Accepted Answer

Maintaining a constant current in a circuit for long periods

Electrical Potential, Electrical Energy, and Capacitance: Study Notes

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