Q: A dipole with moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque experienced by the dipole?

$$\tau = \vec{p} \times \vec{E}$$

Q: Which equation represents Gauss's Law in differential form?

$$\nabla \cdot \vec{E} = \frac{\rho}{\$$epsilon_0$$}$$

Question 1

A point charge $$q is $$placed at the center of a spherical conducting shell of radius $$R. $$What is the electric field at a distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$E = \frac{q}{4\pi\$$epsilon_0$$ r^2$}$$

Question 2

A dipole with moment $$\vec{p} is $$placed in a uniform electric field $$\vec{E}. $$What is the torque experienced by the dipole?

Accepted Answer

$$	au = \vec{p} 	imes \vec{E}$$

Question 3

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 4

A charge $$Q is $$distributed uniformly along a thin rod of length $$L. $$What is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \frac{Q}{L}$$

Question 5

A system consists of two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r. $$What is the total potential energy of the system?

Accepted Answer

$$U = \frac{q_1$ q_2$}{4\pi\$$epsilon_0$$ r}$$

Question 6

If the electric potential $$V at a $$point is known, how can the electric field $$\vec{E} be $$determined?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 7

A conducting sphere of radius $$R$$ carries a total charge $$Q. $$What is the surface charge density $$\sigma on $$the sphere?

Accepted Answer

$$\sigma = \frac{Q}{4\pi R^2$}$$

Question 8

Which of the following statements about Gauss's Law is correct?

Accepted Answer

The net electric flux through a closed surface is proportional to the total charge enclosed.

Question 9

A parallel plate capacitor is connected to a battery. If the plates are moved further apart while keeping the battery connected, what happens to the electric field between the plates?

Accepted Answer

The electric field remains constant.

Question 10

A charge $$q is $$placed in an electric field $$\vec{E}. $$What is the force experienced by the charge?

Accepted Answer

$$\vec{F} = q\vec{E}$$

Question 11

A hollow conducting sphere has a cavity inside it. If a charge $$q is $$placed inside the cavity, what is the induced charge on the inner surface of the cavity?

Accepted Answer

The induced charge is $$-q.$$

Question 12

Which equation represents Gauss's Law in differential form?

Accepted Answer

$$
abla \cdot \vec{E} = \frac{ho}{\$$epsilon_0$$}$$

Question 13

A system of three charges $$q_1$$, $$q_2$$, and $$q_3$$ are placed at the vertices of an equilateral triangle of side $$a. $$What is the total potential energy of the system?

Accepted Answer

$$U = \frac{1}{4\pi\$$epsilon_0$$} \left( \frac{q_1$ q_2$}{a} + \frac{q_1$ q_3$}{a} + \frac{q_2$ q_3$}{a} \right)$$

Question 14

Which of the following best describes the field lines near a positive point charge placed next to a conducting surface?

Accepted Answer

Field lines originate from the charge and terminate perpendicular to the conducting surface.

Question 15

A charge distribution has a potential $$V(x) = kx^2$, where k$ is a constant. What is the electric field at position x$?

Accepted Answer

$$E(x) = -2kx$$

Question 16

A dipole is placed in a non-uniform electric field. Which statement is true about the force and torque on the dipole?

Accepted Answer

The dipole experiences both a net force and a torque.

Question 17

A charge $$q is $$placed at a distance $$d$$ from an infinite conducting plane. What is the potential energy of the system?

Accepted Answer

$$U = -\frac{q^2$}{16\pi\$$epsilon_0$$ d}$$

Question 18

Which scenario best illustrates the application of Gauss's Law for calculating electric fields?

Accepted Answer

Finding the electric field outside a uniformly charged spherical shell.

Question 19

A conducting rod of length $$L is $$placed in a uniform electric field $$E. $$What is the induced surface charge density at the ends of the rod?

Accepted Answer

The ends acquire equal and opposite surface charge densities.

Study Guide: Electric Fields, Gauss's Law, and Electric Potential

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