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

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

Question 1

A proton and an electron are initially separated by a distance $$r_i$$ and are brought closer together to a distance $$r_f. $$What is the change in electric potential energy of the system?

Accepted Answer

$$\Delta U_e = -k_e e^2$ \left( \frac{1}{r_f} - \frac{1}{r_i} \right)$$

Question 2

Which of the following statements about electric potential energy is correct?

Accepted Answer

It depends only on the configuration of the charges, not the path.

Question 3

What is the electric potential at a distance $$r$$ from a point charge $$Q$$?

Accepted Answer

$$V = \frac{kQ}{r}$$

Question 4

A charge $$q$$ moves through a potential difference $$\Delta V. $$What is the change in its potential energy?

Accepted Answer

$$\Delta U = q \Delta V$$

Question 5

An electron is accelerated from rest through a potential difference of $$150 V. $$What is its final kinetic energy in electron-volts (eV)?

Accepted Answer

150 eV

Question 6

Which of the following is true about equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces.

Question 7

Given a uniform electric field $$\vec{E} in $$the $$+y$$ direction, what is the potential difference between $$y=0$$ and $$y=a$$?

Accepted Answer

$$V(a) - V(0) = -Ea$$

Question 8

A conducting sphere is given a net charge. Where does the excess charge reside?

Accepted Answer

On the surface of the sphere

Question 9

Which of the following is a correct statement of Gauss's Law?

Accepted Answer

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

Question 10

A long, straight rod has a uniform charge per unit length $$\lambda. $$Using Gauss's Law, what is the magnitude of the electric field at a distance $$r$$ from the rod?

Accepted Answer

$$E = \frac{\lambda}{2\pi \$$epsilon_0$$ r}$$

Question 11

If the electric field inside a conductor is zero, what can be said about the electric potential inside the conductor?

Accepted Answer

It is constant throughout the conductor.

Question 12

A point charge $$+Q is $$placed at the center of a conducting spherical shell with no net charge. What is the induced charge on the inner surface of the shell?

Accepted Answer

$$-Q$$

Question 13

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

Accepted Answer

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

Question 14

A charge $$q is $$moved from point A to point B in an electric field. The potential at A is $$V_A$$ and at B is $$V_B. $$What is the work done by the electric field?

Accepted Answer

$$W = -q(V_B - V_A)$$

Question 15

Which of the following is NOT a property of conductors in electrostatic equilibrium?

Accepted Answer

The electric field just outside the surface is parallel to the surface.

Question 16

A closed surface encloses a net charge $$Q. If $$the surface is deformed but still encloses the same charge, what happens to the total electric flux through the surface?

Accepted Answer

It remains the same.

Question 17

A system consists of three point charges arranged in a right triangle. Which of the following is true about the total electric potential energy of the system?

Accepted Answer

It is the sum of the potential energies of all unique pairs of charges.

Question 18

Which of the following integrals gives the potential difference between two points $$a$$ and $$b in a $$known electric field?

Accepted Answer

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

Question 19

A positive test charge is placed near a negatively charged conducting sphere. What is the direction of the electric field at the location of the test charge?

Accepted Answer

Toward the sphere

Question 20

Which of the following best explains why Gauss's Law is especially useful for calculating electric fields in cases of high symmetry?

Accepted Answer

It simplifies the calculation by making the electric field constant over the Gaussian surface.

Electric Potential and Gauss’ Law – Study Notes for PHY 131

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