Q: Which of the following is the correct form of Gauss's Law?

$$\displaystyle \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{encl}}}{\$$epsilon_0$$}$$

Question 1

A point charge $$q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$According to Gauss's Law, what is the total electric flux through the surface?

Accepted Answer

$$\displaystyle \Phi_E = \frac{q}{\$$epsilon_0$$}$$

Question 2

The electric field in a region is given by $$\vec{E} = 3z\hat{j} - 4y\hat{k} (in V/m). $$What is the electric flux through the right face ($$x = 3.0 m) of $$the cube shown in the first image, if the cube extends from $$x = 1.0 m to$$ $$x = 3.0 m$$?

Accepted Answer

Zero, because $$\vec{E}$$ has no $$\hat{i}$$ component

Question 3

Which of the following best describes the equipotential surfaces for the potential $$V(x, y, z) = 8x - 4x^2$?

Accepted Answer

Parabolic surfaces in the $$x$$ direction

Question 4

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

$$C = K\$$epsilon_0$$ \frac{A}{d}$$

Question 5

The electric potential $$V at a $$distance $$r$$ from a point charge $$q is $$given by which of the following?

Accepted Answer

$$V = \frac{1}{4\pi\$$epsilon_0$$} \frac{q}{r}$$

Question 6

A spherical mercury droplet of volume $$3.0\ 	ext{mm}^3$$ carries a net charge of $$+3.0\ 	ext{nC}. $$What is the potential at the center of the droplet, assuming the potential is zero at infinite distance?

Accepted Answer

$$34\ 	ext{MV}$$

Question 7

Which of the following statements about conductors in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside a conductor is zero

Question 8

A $$+0.30\ 	ext{C}$$ point charge is placed near an uncharged, thick, spherical silver shell. What is the electric field at a point inside the shell but not at its center?

Accepted Answer

Zero

Question 9

The work done by the electrostatic field on an electron moving from point $$X to $$point $$Y$$ along an equipotential surface is:

Accepted Answer

Zero

Question 10

Which of the following is the correct expression for the electric field in terms of the electric potential $$V$$?

Accepted Answer

$$\vec{E} = -\left( \hat{i} \frac{\partial V}{\partial x} + \hat{j} \frac{\partial V}{\partial y} + \hat{k} \frac{\partial V}{\partial z} \right)$$

Question 11

A network of capacitors is connected to a battery. Which quantity must be the same for all capacitors connected in parallel?

Accepted Answer

Potential difference $$V$$

Question 12

The potential energy of an electric dipole in a uniform electric field is:

Accepted Answer

$$U = -\vec{p} \cdot \vec{E}$$

Question 13

Which of the following is the correct form of Gauss's Law?

Accepted Answer

$$\displaystyle \oint \vec{E} \cdot d\vec{A} = \frac{Q_{	ext{encl}}}{\$$epsilon_0$$}$$

Question 14

A capacitor is charged to a potential $$V$$ and then disconnected from the battery. If the separation between the plates is doubled, what happens to the stored energy?

Accepted Answer

It doubles

Question 15

Which of the following is the correct expression for the potential difference between two points $$a$$ and $$b in an $$electric field?

Accepted Answer

$$V_a - V_b = \int_a^b \vec{E} \cdot d\vec{l}$$

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