Q: A parallel-plate capacitor is charged to a potential difference of $$1.5\ \mathrm{V}$$ and has a capacitance of $$1.0\ \mu\mathrm{F}. $$How much charge is stored on the plates?

$$1.5 \times 10$$^{-6}$$\ \mathrm{C}$$

Question 1

Which of the following equations correctly relates the electric field $$\vec{E} to $$the electric potential $$V in $$one dimension?

Accepted Answer

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

Question 2

A point charge $$q is $$located at the origin. What is the electric potential $$V at a $$distance $$r$$ from the charge, assuming $$V = 0 at $$infinity?

Accepted Answer

$$V = \frac{q}{4\pi\$$epsilon_0$$ r}$$

Question 3

An electron is released from rest at $$x = 2\ \mathrm{m} in $$the potential shown in the graph (potential decreases with increasing $$x$$ beyond $$x=2). $$What does the electron do immediately after being released?

Accepted Answer

It moves to the left with increasing speed

Question 4

Which of the following statements about conductors in electrostatic equilibrium is FALSE?

Accepted Answer

The electric field just outside the surface is parallel to the surface.

Question 5

Two metal spheres are connected by a conducting wire. Which of the following quantities must be the same for both spheres?

Accepted Answer

Potential

Question 6

A battery does $$4.8 	imes 10$$^{-19}$$\ \mathrm{J} of $$work to move a single ion of charge $$1.6 	imes 10$$^{-19}$$\ \mathrm{C}$$ from its negative to positive terminal. What is the emf of the battery?

Accepted Answer

$$4.8\ \mathrm{V}$$

Question 7

Which of the following is the correct expression for the capacitance $$C of a $$parallel-plate capacitor with plate area $$A$$ and separation $$d$$?

Accepted Answer

$$C = \$$epsilon_0$$ \frac{A}{d}$$

Question 8

Three capacitors, $$C_1 = 2$$\ \mu\mathrm{F}$$, C_2$ = 3\ \mu\mathrm{F}$$, and $$C_3 = 4$$\ \mu\mathrm{F}$$, are connected in parallel. What is their equivalent capacitance?

Accepted Answer

$$9\ \mu\mathrm{F}$$

Question 9

Two capacitors, $$C_1 = 3$$\ \mu\mathrm{F}$$ and C_2$ = 6\ \mu\mathrm{F}$$, are connected in series. What is their equivalent capacitance?

Accepted Answer

$$2\ \mu\mathrm{F}$$

Question 10

A particle moves from a point at $$V = 40\ \mathrm{V} to a $$point at $$V = 20\ \mathrm{V}. $$What is the potential difference $$\Delta V$$?

Accepted Answer

$$-20\ \mathrm{V}$$

Question 11

Which of the following best describes the direction of the electric field $$\vec{E}$$ relative to equipotential surfaces?

Accepted Answer

$$\vec{E} is $$always perpendicular to equipotential surfaces.

Question 12

A parallel-plate capacitor is charged to a potential difference of $$1.5\ \mathrm{V}$$ and has a capacitance of $$1.0\ \mu\mathrm{F}. $$How much charge is stored on the plates?

Accepted Answer

$$1.5 	imes 10$$^{-6}$$\ \mathrm{C}$$

Question 13

Which of the following is a consequence of Kirchhoff’s loop law?

Accepted Answer

The sum of all potential differences around a closed loop is zero.

Question 14

If the electric potential $$V(x)$$ decreases linearly from $$60\ \mathrm{V} at$$ $$x = -2\ \mathrm{m} to$$ $$0\ \mathrm{V} at$$ $$x = 4\ \mathrm{m}$$, what is the magnitude and direction of the electric field?

Accepted Answer

$$10\ \mathrm{V/m} to $$the right

Question 15

Which of the following statements about the energy stored in a capacitor is correct?

Accepted Answer

The energy stored is $$U = \frac{1}{2} C V^2$

Question 16

A conductor has a sharp corner. What happens to the electric field and surface charge density at this location?

Accepted Answer

Both are maximized at the corner.

Question 17

Which of the following is true for capacitors connected in series?

Accepted Answer

They all have the same charge.

Question 18

A battery is connected to a parallel-plate capacitor. Which of the following statements is true when the capacitor is fully charged?

Accepted Answer

The potential difference across the capacitor equals the emf of the battery.

Chapter 26: Potential and Field – Study Notes

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