Q: A dipole with moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque $$\vec{\tau} on $$the dipole, and what is the potential energy $$U$$?

$$\vec{\tau} = \vec{p} \times \vec{E}$$; $$U = -\vec{p} \cdot \vec{E}$$

Question 1

Which of the following statements best describes the quantization of electric charge?

Accepted Answer

Electric charge is always a multiple of the elementary charge $$e = 1.602 	imes 10$$^{-19}$$\ \mathrm{C}.$$

Question 2

A glass rod is rubbed with silk, and the rod becomes positively charged. Which process is primarily responsible for this charging, and what happens at the atomic level?

Accepted Answer

Friction (triboelectric effect); electrons are transferred from the glass rod to the silk.

Question 3

Which of the following is NOT a property of the electrostatic force described by Coulomb’s Law?

Accepted Answer

It is a short-range force, acting only at atomic distances.

Question 4

A point charge $$q is $$placed at the center of a hollow, neutral, conducting sphere. What is the net charge on the inner and outer surfaces of the sphere, respectively?

Accepted Answer

Inner: $$-q$$, Outer: $$+q$$

Question 5

A positive test charge $$q_0 is $$placed in an electric field $$\vec{E}. $$What is the force experienced by the test charge, and how does the direction of $$\vec{E}$$ relate to the force?

Accepted Answer

$$\vec{F} = q_0$ \vec{E}$$; the force is in the same direction as $$\vec{E}.$$

Question 6

A particle of mass $$m$$ and charge $$+q$$ enters a region between two large parallel plates with a uniform electric field $$\vec{E}$$ directed downward. If the particle enters with initial velocity $$v_0$$ parallel to the plates, what is the equation for its vertical displacement $$y as a $$function of horizontal position $$x$$?

Accepted Answer

$$y = \dfrac{qE}{2mv_0^2$} x^2$

Question 7

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

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 8

A uniformly charged ring of total charge $$Q$$ and radius $$R$$ lies in the $$xy-$$plane, centered at the origin. What is the electric field at a point on the $$x-$$axis a distance $$x$$ from the center?

Accepted Answer

$$E_x = k_e Q x / (x^2$ + R^2$)^{3/2}$

Question 9

A long, straight wire has a uniform linear charge density $$\lambda. $$Using Gauss’s Law, what is the magnitude of the electric field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 10

A non-conducting solid sphere of radius $$R$$ has a uniform charge density $$\rho. $$What is the electric field at a distance $$r \u003c R$$ from the center of the sphere?

Accepted Answer

$$E = \dfrac{\rho r}{3\$$varepsilon_0$$}$$

Question 11

A dipole with moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque $$\vec{	au} on $$the dipole, and what is the potential energy $$U$$?

Accepted Answer

$$\vec{	au} = \vec{p} 	imes \vec{E}$$; $$U = -\vec{p} \cdot \vec{E}$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following statements about electric field lines is FALSE?

Accepted Answer

Field lines can cross if the electric field is strong enough.

Question 14

A neutral conducting sphere is brought near a negatively charged rod, but does not touch it. The far side of the sphere is then grounded. What is the net charge on the sphere after the ground is removed and the rod is taken away?

Accepted Answer

The sphere is positively charged.

Question 15

A point charge $$+Q is $$placed near a dielectric (insulator). What happens to the dielectric at the molecular level?

Accepted Answer

The dielectric becomes polarized; its molecules develop induced dipoles aligned with the external field.

Question 16

Two point charges, $$q_1 = +2$$\ \mu\mathrm{C}$$ and q_2$ = -2\ \mu\mathrm{C}$$, are separated by a distance $$r. $$What is the direction of the force on $$q_1$$ due to $$q_2$$?

Accepted Answer

Toward $$q_2$$, because unlike charges attract.

Question 17

A charge $$q_0 is $$placed at a point where the electric field due to several other charges is zero. What can be said about the net force on $$q_0$$?

Accepted Answer

The net force on $$q_0 is $$zero.

Question 18

A uniformly charged disk of radius $$R$$ has surface charge density $$\sigma. $$What is the electric field on the axis of the disk at a distance $$x$$ from its center?

Accepted Answer

$$E_x = \dfrac{\sigma}{2\$$varepsilon_0$$} \left(1 - \dfrac{x}{\sqrt{x^2$ + R^2$}}\right)$$

Question 19

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

Accepted Answer

The net electric field at a point is the vector sum of the fields produced by each charge independently.

Electrostatics: Calculus-Based Physics Study Notes

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