Q: A capacitor is constructed with two plates of area $$0.15\,\text{m}^2$$ separated by $$0.25\,\text{mm} in $$air. What is its capacitance?

$$5.4 \times 10$$^{-9}$$\,\text{F}$$

Question 1

Which statement best describes the electric field inside a conductor in electrostatic equilibrium?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 2

Why must the electric field just outside a conductor be perpendicular to its surface?

Accepted Answer

Because parallel fields would cause surface charges to move, violating electrostatic equilibrium.

Question 3

Two conducting spheres of radii $$R_1$$ and $$R_2$$ are connected by a wire and share a total charge $$Q. If$$ $$R_1$$ \u003e $$R_2$$, which sphere has the higher electric field at its surface?

Accepted Answer

The sphere with radius $$R_2.$$

Question 4

A lightning rod works by:

Accepted Answer

Increasing the electric field at its tip to cause air breakdown and discharge before dangerous lightning can form.

Question 5

What happens when a conductor is grounded?

Accepted Answer

Electrons move between the conductor and the Earth until the potential is equalized.

Question 6

A dielectric material is placed between the plates of a capacitor. What is the effect on the net electric field between the plates?

Accepted Answer

The net electric field decreases due to the induced dipole fields opposing the external field.

Question 7

Given the dielectric constant $$\kappa$$ for water is 81, what is the ratio of the electric force between two charges in water compared to the same force in vacuum?

Accepted Answer

The force in water is 81 times smaller than in vacuum.

Question 8

Which equation correctly expresses the capacitance $$C of a $$parallel-plate capacitor with plate area $$A$$, separation $$s$$, and dielectric constant $$\kappa$$?

Accepted Answer

$$C = \frac{\kappa \$$varepsilon_0$$ A}{s}$$

Question 9

A capacitor is constructed with two plates of area $$0.15\,	ext{m}^2$$ separated by $$0.25\,	ext{mm} in $$air. What is its capacitance?

Accepted Answer

$$5.4 	imes 10$$^{-9}$$\,	ext{F}$$

Question 10

What is the effect of increasing the plate area $$A of a $$parallel-plate capacitor while keeping the plate separation $$s$$ constant?

Accepted Answer

The capacitance increases.

Question 11

If the distance $$s$$ between the plates of a parallel-plate capacitor is doubled, what happens to the capacitance?

Accepted Answer

The capacitance is halved.

Question 12

Which material listed below would most effectively reduce the electric field between capacitor plates?

Accepted Answer

Water ($$\kappa = 81)$$

Question 13

A parallel-plate capacitor is connected to a battery and fully charged. If a dielectric with $$\kappa = 4 is $$inserted between the plates, what happens to the stored energy if the battery remains connected?

Accepted Answer

The stored energy increases.

Question 14

Which formula gives the energy density $$u_E of $$the electric field in a capacitor with dielectric constant $$\kappa$$?

Accepted Answer

$$u_E = \frac{1}{2} \kappa \$$varepsilon_0$$ E^2$

Question 15

Capacitors are often connected in series or parallel. Which statement is true for capacitors in parallel?

Accepted Answer

The equivalent capacitance is the sum of the individual capacitances.

Question 16

A capacitor is charged to a voltage $$\Delta V. $$Which equation correctly relates the charge $$Q$$ stored and the capacitance $$C$$?

Accepted Answer

$$Q = C \Delta V$$

Question 17

Which scenario would most likely result in capacitor breakdown?

Accepted Answer

Decreasing the plate separation and increasing the voltage until the electric field exceeds $$3 	imes 10^6$ N/C.

Question 18

A parallel-plate capacitor is charged, then disconnected from the battery. If the plate separation is increased, what happens to the voltage across the plates?

Accepted Answer

The voltage increases.

Question 19

Which equation describes the electric force between two charges $$q_1$$ and $$q_2$$ separated by distance $$r in a $$dielectric medium with constant $$\kappa$$?

Accepted Answer

$$F = k_C \frac{|q_1$||q_2$|}{\kappa r^2$}$$

Charges, Fields, and Capacitors: Conductors, Dielectrics, and Energy Storage

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