Q: A proton is released from rest in a uniform electric field of magnitude $$E = 2.0 \times 10^4$\ \mathrm{N/C}. If $$the proton moves a distance $$d = 0.01\ \mathrm{m} in $$the direction of the field, what is the change in its electric potential energy?

$$\Delta PE = -qEd = -(1.6 \times 10$$^{-19}$$\ \mathrm{C})(2.0 \times 10^4$\ \mathrm{N/C})(0.01\ \mathrm{m}) = -3.2 \times 10$$^{-17}$$\ \mathrm{J}$$

Q: A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}. $$How much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(2.0 \times 10$$^{-6}$$\ \mathrm{F})(12^2$\ \mathrm{V}^2) = 1.44 \times 10$$^{-4}$$\ \mathrm{J}$$

Q: A $$5.0\ \mathrm{V}$$ potential difference is applied across a $$10\ \mathrm{mm}$$ thick dielectric slab with dielectric constant $$K=4$$ and area $$0.01\ \mathrm{m}^2. $$What is the capacitance?

$$C = K\$$varepsilon_0$$ \frac{A}{d} = 4 \times 8.85 \times 10$$^{-12}$$\ \mathrm{F/m} \times \frac{0.01}{0.01} = 3.54 \times 10$$^{-11}$$\ \mathrm{F}$$

Q: A heart defibrillator uses a capacitor charged to $$4000\ \mathrm{V}$$ with a capacitance of $$100\ \mu\mathrm{F}. $$How much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(100 \times 10$$^{-6}$$\ \mathrm{F})(4000^2$\ \mathrm{V}^2) = 800\ \mathrm{J}$$

Q: A $$+2\ \mu\mathrm{C}$$ charge is moved from a point at $$V=10\ \mathrm{V} to a $$point at $$V=0\ \mathrm{V}. $$What is the work done by the electric field?

$$W = -q(V_b - V_a) = -(2 \times 10$$^{-6}$$\ \mathrm{C})(0 - 10\ \mathrm{V}) = 2 \times 10$$^{-5}$$\ \mathrm{J}$$

Question 1

A proton is released from rest in a uniform electric field of magnitude $$E = 2.0 	imes 10^4$\ \mathrm{N/C}. If $$the proton moves a distance $$d = 0.01\ \mathrm{m} in $$the direction of the field, what is the change in its electric potential energy?

Accepted Answer

$$\Delta PE = -qEd = -(1.6 	imes 10$$^{-19}$$\ \mathrm{C})(2.0 	imes 10^4$\ \mathrm{N/C})(0.01\ \mathrm{m}) = -3.2 	imes 10$$^{-17}$$\ \mathrm{J}$$

Question 2

Which of the following statements about equipotential surfaces is correct?

Accepted Answer

Electric field lines are always perpendicular to equipotential surfaces.

Question 3

A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(2.0 	imes 10$$^{-6}$$\ \mathrm{F})(12^2$\ \mathrm{V}^2) = 1.44 	imes 10$$^{-4}$$\ \mathrm{J}$$

Question 4

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

Accepted Answer

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

Question 5

A parallel-plate capacitor has plate area $$A$$ and separation $$d. $$What is the capacitance if the space between the plates is filled with a dielectric of constant $$K$$?

Accepted Answer

$$C = K\$$varepsilon_0$$ \frac{A}{d}$$

Question 6

Which of the following best describes the energy density in an electric field?

Accepted Answer

$$u = \frac{1}{2}\$$varepsilon_0$$ E^2$

Question 7

A $$5.0\ \mathrm{V}$$ potential difference is applied across a $$10\ \mathrm{mm}$$ thick dielectric slab with dielectric constant $$K=4$$ and area $$0.01\ \mathrm{m}^2. $$What is the capacitance?

Accepted Answer

$$C = K\$$varepsilon_0$$ \frac{A}{d} = 4 	imes 8.85 	imes 10$$^{-12}$$\ \mathrm{F/m} 	imes \frac{0.01}{0.01} = 3.54 	imes 10$$^{-11}$$\ \mathrm{F}$$

Question 8

Which of the following is true about the electron volt (eV)?

Accepted Answer

It is the energy gained by an electron moving through a potential difference of $$1\ \mathrm{V}.$$

Question 9

A digital audio signal must be converted back to analog before being sent to a loudspeaker. Why is this necessary?

Accepted Answer

Loudspeakers require continuously varying voltages to produce sound waves.

Question 10

A heart defibrillator uses a capacitor charged to $$4000\ \mathrm{V}$$ with a capacitance of $$100\ \mu\mathrm{F}. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2}(100 	imes 10$$^{-6}$$\ \mathrm{F})(4000^2$\ \mathrm{V}^2) = 800\ \mathrm{J}$$

Question 11

Which of the following is a correct statement about the relationship between electric potential and electric field in a uniform field?

Accepted Answer

$$E = -\frac{V_{ba}}{d}$$

Question 12

A $$+2\ \mu\mathrm{C}$$ charge is moved from a point at $$V=10\ \mathrm{V} to a $$point at $$V=0\ \mathrm{V}. $$What is the work done by the electric field?

Accepted Answer

$$W = -q(V_b - V_a) = -(2 	imes 10$$^{-6}$$\ \mathrm{C})(0 - 10\ \mathrm{V}) = 2 	imes 10$$^{-5}$$\ \mathrm{J}$$

Question 13

Which of the following is a property of a dielectric material placed between the plates of a capacitor?

Accepted Answer

It increases the capacitance by reducing the effective electric field.

Question 14

The electric potential due to an electric dipole at a distant point is proportional to:

Accepted Answer

$$\frac{1}{r^2$}$$

Question 15

Which of the following best explains why digital signals are less sensitive to noise than analog signals?

Accepted Answer

Digital signals use discrete voltage levels, making small fluctuations less likely to cause errors.

Question 16

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

The stored energy decreases because the capacitance increases but the charge remains constant.

Question 17

Which of the following is true about the surface of a conductor in electrostatic equilibrium?

Accepted Answer

It is an equipotential surface.

Question 18

A CRT (cathode ray tube) in a TV uses electric fields to steer electrons. What is the physical principle that allows the electrons to be deflected?

Accepted Answer

Electrons experience a force when moving through an electric field, given by $$F = qE.$$

Question 19

Which of the following is the correct formula for the capacitance of a parallel-plate capacitor in vacuum?

Accepted Answer

$$C = \$$varepsilon_0$$ \frac{A}{d}$$

Electric Potential and Capacitance: Principles and Applications (Chapter 17 Study Notes)

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