Electric Charges and Fields

Topics in this chapter

• Coulomb Forces and Superposition
• Charged-Particle Equilibrium and Motion
• Electric Dipoles in Fields
• Gauss's Law and Electric Flux
• Conductors and Electrostatic Induction
• Continuous Charge Distributions
• Field Lines and Electric Potential

Cheat sheet

Practice questions

1. Question 1Q-39F68B

   A point charge $q$ is placed at a distance $a/2$ directly above the center of a square of side $a$. The total electric flux through the square is:

   1. A.$\frac{q}{6\varepsilon_0}$
   2. B.$\frac{q}{\varepsilon_0}$
   3. C.$\frac{q}{4\varepsilon_0}$
   4. D.$\frac{q}{2\varepsilon_0}$
   See the answer and solution
2. Question 2Q-9A89F2

   An electric dipole of dipole moment $P$ is placed in a uniform electric field $E$ with its axis making an angle of $37^\circ$ with the field. The work required to rotate the dipole until it is aligned antiparallel to the electric field is:

   1. A.$-PE(0.2)$
   2. B.$PE(1.8)$
   3. C.$PE(1.2)$
   4. D.$PE(0.8)$
   See the answer and solution
3. Question 3Q-DA4094

   A thin spherical shell of radius $R$ has a total charge $Q$ uniformly distributed over its surface. Which of the following graphs best represents the variation of magnitude of electric field $E$ with distance $r$ from the center?

   1. A.$E = 0$ for $r < R$, and decreases as $1/r^2$ for $r \ge R$
   2. B.$E$ increases linearly for $r < R$, and decreases as $1/r$ for $r \ge R$
   3. C.$E$ is constant for $r < R$, and decreases as $1/r$ for $r \ge R$
   4. D.$E$ decreases as $1/r^2$ for all values of $r$
   See the answer and solution
4. Question 4Q-AFF05C

   Two point charges $q$ and $-3q$ are placed at a distance $l$ apart on the $x$-axis. At what coordinate on the $x$-axis (measured from charge $q$) is the net electric field zero?

   1. A.$\frac{l}{\sqrt{3}-1}$ to the left of $q$
   2. B.$\frac{l}{\sqrt{3}+1}$ to the right of $q$
   3. C.$\frac{l}{\sqrt{3}-1}$ to the right of $q$
   4. D.$\frac{l}{\sqrt{3}+1}$ to the left of $q$
   See the answer and solution
5. Question 5Q-FB1EB2

   A non-conducting infinite solid cylinder of radius $R$ carries a volume charge density $\rho$ that varies with radial distance $r$ from the axis as $\rho = \rho_0 r$ (where $\rho_0$ is a constant). The electric field at a distance $r$ ($r < R$) from the axis is:

   1. A.$\frac{\rho_0 r^2}{3\varepsilon_0}$
   2. B.$\frac{\rho_0 r}{3\varepsilon_0}$
   3. C.$\frac{\rho_0 r^2}{2\varepsilon_0}$
   4. D.$\frac{\rho_0 r}{2\varepsilon_0}$
   See the answer and solution