Question 1

A positive charge moves in the direction of a uniform electric field. Which statement is true about the work done by the electric field?

Accepted Answer

The electric field does positive work on the charge.

Question 2

Which equation correctly expresses the electric potential energy $$U of a $$charge $$q in a $$uniform electric field $$E$$ over a distance $$x$$?

Accepted Answer

$$U = U_0$ - qEx$$

Question 3

A battery is connected across two large parallel plates separated by $$d = 9.0\ \mathrm{mm}$$, creating a potential difference of $$V = 9.0\ \mathrm{V}. An $$electron is released at the negative plate. What is its speed just before it hits the positive plate? (Electron mass $$m = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$, charge $$e = 1.60 	imes 10$$^{-19}$$\ \mathrm{C})$$

Accepted Answer

$$v = \sqrt{2eV/m}$$

Question 4

Which of the following is the correct formula for the electric potential $$V at a $$distance $$r$$ from a point charge $$Q$$?

Accepted Answer

$$V = k\dfrac{Q}{r}$$

Question 5

Three point charges are arranged in a line: $$2.0\ \mathrm{nC}$$, $$1.0\ \mathrm{nC}$$, and $$-3.0\ \mathrm{nC}$$, each separated by $$1.0\ \mathrm{m}. $$What is the total electric potential energy stored in this configuration?

Accepted Answer

$$U = -36\ \mathrm{nJ}$$

Question 6

Consider two charges: $$+q at $$distance $$r$$ from $$+Q ($$position A), and $$+2q at $$distance $$2r$$ from $$+Q ($$position B). Compare the electric potential energy at A and B.

Accepted Answer

The potential energy at A is the same as at B.

Question 7

For a parallel-plate capacitor with plate area $$A$$ and separation $$d$$, what is the correct formula for its capacitance $$C in $$vacuum?

Accepted Answer

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

Question 8

If the plates of a parallel-plate capacitor are moved closer together while the capacitor is disconnected from the battery, what happens to the charge on each plate?

Accepted Answer

The charge stays the same.

Question 9

A parallel-plate capacitor is connected to a battery and then a dielectric is inserted between the plates. What happens to the voltage across the plates if the charge is kept constant?

Accepted Answer

The voltage decreases.

Question 10

Two capacitors, $$C_1 = 12.0$$\ \mathrm{nF}$$ and C_2$ = 6.0\ \mathrm{nF}$$, are connected in series across an $$18\ \mathrm{V}$$ battery. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = 4.0\ \mathrm{nF}$$

Question 11

Two identical capacitors, each of capacitance $$C$$, are connected in series. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = C/2$$

Question 12

Two capacitors, $$C_1 = 10$$\ \mathrm{\mu F}$$ and C_2$ = 20\ \mathrm{\mu F}$$, are connected in parallel. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = 30\ \mathrm{\mu F}$$

Question 13

A parallel-plate capacitor is charged to a potential $$V$$ and then disconnected from the battery. If the plate separation is increased, what happens to the energy stored in the capacitor?

Accepted Answer

The energy increases.

Question 14

What is the energy density $$u$$ stored in the electric field between the plates of a parallel-plate capacitor?

Accepted Answer

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

Question 15

A capacitor of $$1\ \mathrm{\mu F} is $$attached in series with a capacitor of $$1\ \mathrm{F}. $$What is the effective capacitance?

Accepted Answer

Very close to $$1\ \mathrm{\mu F}$$

Question 16

A capacitor of $$1\ \mathrm{\mu F} is $$attached in parallel with a capacitor of $$1\ \mathrm{F}. $$What is the effective capacitance?

Accepted Answer

Very close to $$1.000001\ \mathrm{F}$$

Question 17

If a dielectric with dielectric constant $$K is $$inserted between the plates of a capacitor, which statement is true?

Accepted Answer

$$K is $$greater than 1.

Question 18

Which of the following statements about electric field lines and equipotential surfaces is correct?

Accepted Answer

Electric field lines are always perpendicular to equipotential surfaces.

Question 19

A charge of $$1.0\ \mathrm{C} is $$moved from point $$X to $$point $$Y$$, where the potential at $$X is$$ $$40\ \mathrm{V}$$ and at $$Y is$$ $$-20\ \mathrm{V}. $$How much work is done by the electric field?

Accepted Answer

$$W = 60\ \mathrm{J}$$

Electric Potential and Capacitance: Study Notes

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