Q: A $$1\ \text{mm} \times 1\ \text{mm}$$ parallel-plate capacitor is separated by $$1\ \mu\text{m}. $$What is its capacitance?

$$C = 8.85 \times 10$$^{-12}$$\ \frac{A}{d}$$

Question 1

A battery like the one shown in the image has a voltage of 1.5 V. If it is used to charge a capacitor, what is the potential difference across the capacitor when fully charged?

Accepted Answer

$$1.5\ 	ext{V}$$

Question 2

Given the graph of $$E_x$$ versus $$x ($$second image), what is the expression for the electric potential difference $$\Delta V$$ between $$x=0$$ and $$x$$?

Accepted Answer

$$\Delta V = -500x^2$

Question 3

Which equation correctly relates the electric potential difference to the electric field along a path?

Accepted Answer

$$\Delta V = V_f - V_i = -\int_{s_i}^{s_f} E_s ds = -\int_{i}^{f} \vec{E} \cdot d\vec{s}$$

Question 4

If the electric field $$E_x$$ increases linearly with $$x as $$shown, what is the electric potential $$V(x)$$?

Accepted Answer

$$V(x) = -500x^2$

Question 5

A charge $$q is $$moved a small distance $$\Delta s in $$the direction of the electric field $$\vec{E}. $$What is the work done by the field?

Accepted Answer

$$W = q E_s \Delta s$$

Question 6

For a ring of charge, the electric potential at a point on the $$z-$$axis is $$V_z = \frac{Q}{4\pi\$$epsilon_0$$ \sqrt{R^2$ + z^2$}}. $$What is the $$z-$$component of the electric field at that point?

Accepted Answer

$$E_z = \frac{Qz}{4\pi\$$epsilon_0$$ (R^2$ + z^2$)^{3/2}$$}$

Question 7

Which statement about equipotential surfaces and electric fields is correct?

Accepted Answer

The electric field is perpendicular to equipotential surfaces.

Question 8

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d. $$What is its capacitance?

Accepted Answer

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

Question 9

If two capacitors $$C_1$$ and $$C_2$$ are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$$C_{eq} = C_1$ + C_2$

Question 10

If two capacitors $$C_1$$ and $$C_2$$ are connected in series, what is the equivalent capacitance?

Accepted Answer

$$C_{eq} = \frac{C_1$ C_2$}{C_1$ + C_2$}$$

Question 11

A $$1\ 	ext{mm} 	imes 1\ 	ext{mm}$$ parallel-plate capacitor is separated by $$1\ \mu	ext{m}. $$What is its capacitance?

Accepted Answer

$$C = 8.85 	imes 10$$^{-12}$$\ \frac{A}{d}$$

Question 12

When a capacitor is fully charged by a battery, what happens to the current in the circuit?

Accepted Answer

The current stops flowing.

Question 13

In a circuit with three metal spheres of different radii connected by a wire, which statement is true at electrostatic equilibrium?

Accepted Answer

All spheres have the same potential at their surfaces.

Question 14

Which potential graph (from the images) describes the electric field pointing upward along the $$y-$$axis?

Accepted Answer

Graph (a): $$V$$ increases linearly with $$y$$

Question 15

Where is the electric field strongest in a region with equipotential lines?

Accepted Answer

Where the equipotential lines are closest together.

Question 16

Rank the equivalent capacitances for the four capacitor arrangements shown (last image) from smallest to largest.

Accepted Answer

(c) \u003c (a) = (d) \u003c (b)

Question 17

For a conductor in electrostatic equilibrium, which statement is correct?

Accepted Answer

The electric field inside the conductor is zero.

Question 18

If the electric field is given by $$E = -\frac{dV}{dx}$$, what does a positive slope of $$V(x)$$ indicate about the direction of $$E$$?

Accepted Answer

The electric field points in the direction of decreasing $$x.$$

Electric Potential, Electric Field, and Capacitance Ch 26

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