Question 1

A glass rod is rubbed with silk, resulting in the rod becoming positively charged. Which of the following best explains this phenomenon?

Accepted Answer

Electrons are transferred from the rod to the silk, leaving the rod positively charged.

Question 2

Two point charges, $$q_1 = +2$$ \ \mu\mathrm{C}$$ and q_2$ = -3 \ \mu\mathrm{C}$$, are placed 0.5 m apart in vacuum. What is the magnitude of the force between them? (Use $$k = 8.99 	imes 10^9$ \ \mathrm{N\cdot m^2$/C^2$$}$)

Accepted Answer

$$F = 0.216 \ \mathrm{N}$$

Question 3

Three charges are placed at the corners of an equilateral triangle of side $$a. $$Each charge is $$+Q. $$What is the magnitude of the net force on any one charge?

Accepted Answer

$$F = \frac{\sqrt{3} Q^2$}{4\pi\$$varepsilon_0$$ a^2$}$$

Question 4

A point charge $$+Q is $$placed at the center of a spherical conducting shell of inner radius $$a$$ and outer radius $$b. $$The shell is initially uncharged. What is the charge induced on the inner surface of the shell?

Accepted Answer

$$-Q$$

Question 5

Which of the following statements about the electric field inside a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 6

A uniformly charged infinite plane has a surface charge density $$\sigma. $$What is the magnitude of the electric field just above the plane?

Accepted Answer

$$E = \frac{\sigma}{2\$$varepsilon_0$$}$$

Question 7

A parallel plate capacitor is connected to a battery and fully charged. The battery is then disconnected, and a dielectric slab is inserted between the plates. What happens to the voltage across the plates?

Accepted Answer

The voltage decreases.

Question 8

A long straight wire carries a uniform linear charge density $$\lambda. $$What is the magnitude of the electric field at a distance $$r$$ from the wire?

Accepted Answer

$$E = \frac{\lambda}{2\pi\$$varepsilon_0$$ r}$$

Question 9

Which of the following best describes the principle of superposition for electric fields?

Accepted Answer

The total electric field at a point is the sum of the fields due to each charge.

Question 10

A $$2\ \mu\mathrm{F}$$ capacitor and a $$4\ \mu\mathrm{F}$$ capacitor are connected in series across a $$12\ \mathrm{V}$$ battery. What is the voltage across the $$4\ \mu\mathrm{F}$$ capacitor?

Accepted Answer

$$8\ \mathrm{V}$$

Question 11

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

Accepted Answer

$$V = \frac{q}{4\pi\$$varepsilon_0$$ r}$$

Question 12

A charged particle moves from point A to point B in a uniform electric field $$\vec{E}. $$The displacement vector from A to B is $$\vec{d}. $$What is the change in electric potential?

Accepted Answer

$$\Delta V = -\vec{E} \cdot \vec{d}$$

Question 13

A parallel plate capacitor has plates of area $$A$$ separated by distance $$d$$ and filled with a dielectric of constant $$k. $$What is the capacitance?

Accepted Answer

$$C = \frac{k\$$varepsilon_0$$ A}{d}$$

Question 14

A metal sphere of radius $$R$$ carries a total charge $$Q. $$What is the electric field at a distance $$r$$ from the center, where $$r \u003e R$$?

Accepted Answer

$$E = \frac{Q}{4\pi\$$varepsilon_0$$ r^2$}$$

Question 15

A capacitor is connected to a battery and reaches full charge. If the plate separation is doubled while the battery remains connected, what happens to the stored energy?

Accepted Answer

The stored energy is halved.

Question 16

A non-conducting rod of length $$L$$ has a uniform charge density $$\lambda. $$What is the electric field at a point on the perpendicular bisector a distance $$a$$ from the center of the rod?

Accepted Answer

$$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{2\lambda}{a} \frac{L}{\sqrt{a^2$ + (L/2)^2$}}$$

Question 17

Which of the following is true about the conservation of charge?

Accepted Answer

The total charge in an isolated system remains constant.

Question 18

A $$5\ \mu\mathrm{F}$$ capacitor is charged to $$10\ \mathrm{V}$$ and then disconnected from the battery. If the plates are pulled apart so the capacitance drops to $$2\ \mu\mathrm{F}$$, what is the new voltage across the plates?

Accepted Answer

$$25\ \mathrm{V}$$

Question 19

Which of the following best describes the relationship between electric field and electric potential?

Accepted Answer

The electric field is the negative gradient of the electric potential.

Question 20

A parallel plate capacitor is filled halfway with a dielectric of constant $$k ($$the other half is vacuum). If the original capacitance was $$C_0$$, what is the new capacitance?

Accepted Answer

$$C = \frac{2k}{k+1} C_0$

Electrostatics and Capacitance: Key Concepts and Applications

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