Electric Forces and Fields — Hard Practice Quiz

A Physics cheat sheet for Electric Forces and Fields — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Practice quiz

1. A point charge $q_1$ creates an electric field. A second point charge $q_2$ is placed at a distance $r$ from $q_1$, experiencing a force of magnitude $F$. If $q_2$ is then replaced by a test charge $q_0$ at the same distance $r$, what is the magnitude of the electric field $E$ at that point in terms of $F$, $q_1$, and $q_2$?

   • $\frac{F}{q_0}$
   • $\frac{F}{q_2}$
   • $\frac{F q_0}{q_2}$
   • $\frac{F q_2}{q_0}$

   Answer: $\frac{F}{q_2}$

2. A point charge $Q$ is located at the center of a cube with side length $L$. What is the magnitude of the electric flux through one face of the cube?

   • $\frac{Q}{\epsilon_0}$
   • $\frac{Q}{6\epsilon_0}$
   • $\frac{Q L^2}{\epsilon_0}$
   • $\frac{Q}{L^2 \epsilon_0}$

   Answer: $\frac{Q}{6\epsilon_0}$

3. Two point charges, $q_A = +2q$ and $q_B = -q$, are separated by a distance $d$. At what distance from $q_B$ (along the line connecting them or its extension) is the net electric field zero?

   • $d(\sqrt{2}-1)$
   • $d(\sqrt{2}+1)$
   • $\frac{d}{\sqrt{2}}$
   • $\frac{d}{2}$

   Answer: $d(\sqrt{2}+1)$

4. A uniform electric field of magnitude $E$ passes through a circular disk of radius $R$. If the electric field lines are parallel to the plane of the disk, what is the electric flux through the disk?

   • $E \pi R^2$
   • $\frac{E \pi R^2}{2}$
   • $0$
   • $E \pi R^2 \cos(45^\circ)$

   Answer: $0$

5. A spherical Gaussian surface encloses a net charge $Q$. If the radius of the Gaussian surface is doubled, and simultaneously, the enclosed charge is halved, how does the net electric flux through the surface change?

   • It doubles.
   • It is halved.
   • It remains the same.
   • It is quartered.

   Answer: It is halved.

6. An electric field $E$ is produced by a point charge $q$. If a test charge $q_0$ is placed at a distance $r$ from $q$, it experiences a force $F$. If the distance $r$ is doubled, and the magnitude of $q$ is also doubled, how does the force $F$ on $q_0$ change?

   • It doubles.
   • It is halved.
   • It remains the same.
   • It is quartered.

   Answer: It is halved.

7. A point charge $q$ is placed at the origin. A spherical Gaussian surface of radius $R$ is centered at $x=2R$ on the x-axis. What is the net electric flux through this Gaussian surface?

   • $\frac{q}{\epsilon_0}$
   • $\frac{q}{2\epsilon_0}$
   • $0$
   • $\frac{q}{4\pi R^2 \epsilon_0}$

   Answer: $0$

8. A uniform electric field of magnitude $E = 100 \text{ N/C}$ passes through a flat square surface of side length $2.0 \text{ m}$. If the electric flux through the surface is $100 \text{ N} \cdot \text{m}^2/\text{C}$, what is the angle $\phi$ between the electric field vector and the normal to the surface?

   • $\arccos(1)$
   • $\arccos(0.5)$
   • $\arccos(0.25)$
   • $\arccos(0)$

   Answer: $\arccos(0.25)$

9. Two identical positive point charges, each of magnitude $q$, are separated by a distance $2r$. What is the magnitude of the net electric field at the midpoint between them?

   • $0$
   • $k \frac{q}{r^2}$
   • $2k \frac{q}{r^2}$
   • $k \frac{q}{(2r)^2}$

   Answer: $0$

10. A charge $Q$ is uniformly distributed over a very large, thin, non-conducting sheet, creating a uniform electric field perpendicular to the sheet with magnitude $E = \frac{\sigma}{2\epsilon_0}$, where $\sigma$ is the surface charge density. If a point charge $q_0$ is placed at a distance $d$ from this sheet, what is the magnitude of the force it experiences?

    • $q_0 \frac{\sigma}{2\epsilon_0}$
    • $q_0 \frac{\sigma}{2\epsilon_0 d^2}$
    • $\frac{\sigma}{2\epsilon_0}$
    • $\frac{Q q_0}{4\pi \epsilon_0 d^2}$

    Answer: $q_0 \frac{\sigma}{2\epsilon_0}$