Q: A parallel-plate capacitor has plates of area $$0.2\,\mathrm{m}^2$$ separated by $$1\,\mathrm{mm} of $$glass ($$\kappa = 5). $$What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\,\mathrm{F/m})$$

$$C = 8.85 \times 10$$^{-9}$$\,\mathrm{F}$$

Question 1

Which of the following statements best describes the electric field inside a conductor in electrostatic equilibrium?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 2

A charged conductor has a cavity inside it. What is the electric field inside the cavity if the conductor is in electrostatic equilibrium and there are no charges inside the cavity?

Accepted Answer

It is zero.

Question 3

Two conducting spheres of radii $$R_1$$ and $$R_2$$ are connected by a conducting wire and brought to the same potential. If $$R_1$$ \u003e $$R_2$$, which sphere will have the higher surface charge density?

Accepted Answer

The sphere with radius $$R_2.$$

Question 4

Why are lightning rods pointed?

Accepted Answer

To increase the electric field at the tip, causing air to ionize and discharge before a large strike.

Question 5

A parallel-plate capacitor is filled with a dielectric material of constant $$\kappa. $$How does the capacitance change compared to the same capacitor with air between the plates?

Accepted Answer

It increases by a factor of $$\kappa.$$

Question 6

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

Accepted Answer

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

Question 7

A capacitor is charged to a voltage $$\Delta V$$ and then disconnected from the battery. If a dielectric is inserted between the plates, what happens to the stored energy?

Accepted Answer

It decreases.

Question 8

The force between two charges $$q_1$$ and $$q_2$$ separated by a distance $$r in a $$dielectric medium is given by:

Accepted Answer

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

Question 9

Which material would most effectively reduce the electric field between the plates of a capacitor, based on its dielectric constant?

Accepted Answer

Water ($$\kappa = 81)$$

Question 10

A parallel-plate capacitor has plates of area $$0.2\,\mathrm{m}^2$$ separated by $$1\,\mathrm{mm} of $$glass ($$\kappa = 5). $$What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\,\mathrm{F/m})$$

Accepted Answer

$$C = 8.85 	imes 10$$^{-9}$$\,\mathrm{F}$$

Question 11

Which of the following best explains why the electric field just outside a conductor is perpendicular to the surface?

Accepted Answer

Because any parallel component would cause surface currents, violating electrostatic equilibrium.

Question 12

If the voltage between two conductors is reduced, what happens to the energy stored in the electric field between them?

Accepted Answer

It decreases.

Question 13

A dielectric material is placed between the plates of a charged capacitor. Which of the following statements is true?

Accepted Answer

The net electric field inside the capacitor decreases.

Question 14

Which of the following equations gives the energy density $$u_E$$ stored in the electric field of a parallel-plate capacitor with dielectric constant $$\kappa$$?

Accepted Answer

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

Question 15

Which of the following changes will increase the capacitance of a parallel-plate capacitor?

Accepted Answer

Inserting a material with a higher dielectric constant.

Question 16

A capacitor is constructed with two plates of area $$A$$ separated by a distance $$s. If $$the area is doubled and the separation is halved, how does the capacitance change?

Accepted Answer

It increases by a factor of 4.

Question 17

Which of the following best describes the effect of grounding a charged conductor?

Accepted Answer

It allows excess charge to flow to or from the Earth, neutralizing the conductor.

Question 18

A parallel-plate capacitor is connected to a battery and fully charged. If the separation between the plates is increased while the battery remains connected, what happens to the charge on the plates?

Accepted Answer

It decreases.

Question 19

Which of the following is a correct expression for the work $$W$$ required to move the plates of a capacitor a distance $$\Delta s$$ apart, given charge $$Q$$ and plate area $$A$$?

Accepted Answer

$$W = \dfrac{Q^2$}{2A\$$varepsilon_0$$} \Delta s$$

Electric Fields, Conductors, Dielectrics, and Capacitors: Study Notes

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