Q: A proton is released from rest at the positive plate of a parallel-plate capacitor and accelerates toward the negative plate. If the potential difference between the plates is $$1000\ \mathrm{V}$$ and the distance between the plates is $$0.02\ \mathrm{m}$$, what is the magnitude of the electric field between the plates?

$$2 \times 10^4$\ \mathrm{V/m}$$

Q: A $$12\ \mathrm{V}$$ battery moves $$7.5 \times 10$$^{21}$$ electrons through a headlight. How much total energy is delivered by the battery?

$$1.44 \times 10^4$\ \mathrm{J}$$

Q: A parallel-plate capacitor has plates of area $$0.2\ \mathrm{m}^2$$ separated by $$1\ \mathrm{mm} of $$air. What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\ \mathrm{C^2$/N\cdot m^2$})$$

$$1.77 \times 10$$^{-9}$$\ \mathrm{F}$$

Q: A living cell membrane is $$8.0\ \mathrm{nm}$$ thick and has an electric field of $$5.5 \times 10^6$\ \mathrm{V/m}$$ across it. What is the potential difference across the membrane?

$$4.4 \times 10$$^{-2}$$\ \mathrm{V}$$

Q: A $$+2\ \mathrm{\mu C}$$ charge is moved from a point at $$10\ \mathrm{V} to a $$point at $$0\ \mathrm{V}. $$What is the change in electric potential energy?

$$-2 \times 10$$^{-5}$$\ \mathrm{J}$$

Q: A defibrillator uses a capacitor to deliver a shock to a patient. If the capacitor stores $$400\ \mathrm{J} of $$energy at $$2000\ \mathrm{V}$$, what is its capacitance?

$$2 \times 10$$^{-4}$$\ \mathrm{F}$$

Question 1

A proton is released from rest at the positive plate of a parallel-plate capacitor and accelerates toward the negative plate. If the potential difference between the plates is $$1000\ \mathrm{V}$$ and the distance between the plates is $$0.02\ \mathrm{m}$$, what is the magnitude of the electric field between the plates?

Accepted Answer

$$2 	imes 10^4$\ \mathrm{V/m}$$

Question 2

Which of the following statements about equipotential surfaces is correct?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 3

A $$12\ \mathrm{V}$$ battery moves $$7.5 	imes 10$$^{21}$$ electrons through a headlight. How much total energy is delivered by the battery?

Accepted Answer

$$1.44 	imes 10^4$\ \mathrm{J}$$

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 plates of area $$0.2\ \mathrm{m}^2$$ separated by $$1\ \mathrm{mm} of $$air. What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{C^2$/N\cdot m^2$})$$

Accepted Answer

$$1.77 	imes 10$$^{-9}$$\ \mathrm{F}$$

Question 6

If a dielectric with $$\kappa = 4 is $$inserted between the plates of a capacitor, what happens to the capacitance?

Accepted Answer

It increases by a factor of 4.

Question 7

Which of the following best describes the energy stored in a capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Question 8

A $$2\ \mathrm{\mu F}$$ and a $$4\ \mathrm{\mu F}$$ capacitor are connected in series. What is their equivalent capacitance?

Accepted Answer

$$1.33\ \mathrm{\mu F}$$

Question 9

A living cell membrane is $$8.0\ \mathrm{nm}$$ thick and has an electric field of $$5.5 	imes 10^6$\ \mathrm{V/m}$$ across it. What is the potential difference across the membrane?

Accepted Answer

$$4.4 	imes 10$$^{-2}$$\ \mathrm{V}$$

Question 10

Which of the following is true about the direction of the electric field between two parallel plates with a potential difference?

Accepted Answer

It points from the plate at higher potential to the plate at lower potential.

Question 11

A $$0.01\ \mathrm{F}$$ parallel-plate capacitor is connected to a $$12\ \mathrm{V}$$ battery. What is the charge stored on the plates?

Accepted Answer

$$0.12\ \mathrm{C}$$

Question 12

Which of the following is the correct relationship between electric potential energy and electric potential?

Accepted Answer

$$PE = qV$$

Question 13

A $$+2\ \mathrm{\mu C}$$ charge is moved from a point at $$10\ \mathrm{V} to a $$point at $$0\ \mathrm{V}. $$What is the change in electric potential energy?

Accepted Answer

$$-2 	imes 10$$^{-5}$$\ \mathrm{J}$$

Question 14

Which of the following is a correct statement about capacitors in parallel?

Accepted Answer

They have the same voltage across each capacitor.

Question 15

A defibrillator uses a capacitor to deliver a shock to a patient. If the capacitor stores $$400\ \mathrm{J} of $$energy at $$2000\ \mathrm{V}$$, what is its capacitance?

Accepted Answer

$$2 	imes 10$$^{-4}$$\ \mathrm{F}$$

Question 16

Which of the following best describes the effect of inserting a dielectric material between the plates of a charged capacitor (with battery disconnected)?

Accepted Answer

The voltage across the plates decreases.

Question 17

What is the energy density $$u$$ stored in an electric field $$E in $$vacuum?

Accepted Answer

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

Question 18

A point charge $$Q is $$placed at the center of a set of concentric equipotential surfaces. What is the potential at a distance $$r$$ from the charge if $$Q = 1\ \mathrm{nC}$$ and $$r = 1\ \mathrm{cm}$$? ($$k = 9 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$)

Accepted Answer

$$9 	imes 10^5$\ \mathrm{V}$$

Question 19

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 $$1\ \mathrm{V}.$$

Chapter 17: Electric Potential and Capacitance – Study Notes

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