Question 1

A point charge $q$ is placed at the center of a spherical surface of radius $r$. What is the electric flux $\Phi_E$ through the surface?

Accepted Answer

$\Phi_E = \dfrac{q}{\epsilon_0}$

Question 2

Two parallel conducting rods of length $L$ and $2L$ have resistances $R$ and $8R$, respectively. If the rods are made of the same material and have circular cross-sections, what is the ratio of their cross-sectional areas $A_1/A_2$?

Accepted Answer

$8$

Question 3

A capacitor is charged to a potential difference $V$ and then disconnected from the battery. If a dielectric is inserted between its plates, what happens to the stored energy $U$ and the capacitance $C$?

Accepted Answer

$U$ decreases, $C$ increases

Question 4

Three point charges $+q$, $-q$, and $+q$ are placed at the corners of an equilateral triangle of side $a$. What is the magnitude of the net electric field at the midpoint of the side joining the two $+q$ charges?

Accepted Answer

$\dfrac{4kq}{a^2}$

Question 5

A parallel plate capacitor with plate area $A$ and separation $d$ is filled with a dielectric of constant $K$. What is the capacitance $C$?

Accepted Answer

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

Question 6

A battery with emf $\mathcal{E}$ and internal resistance $r$ is connected to a resistor $R$. If the terminal voltage is $V$, which equation correctly relates these quantities?

Accepted Answer

$V = \mathcal{E} - Ir$

Question 7

A proton moves in a uniform magnetic field $\vec{B}$ directed into the page. If the proton's velocity $\vec{v}$ is to the right, what is the direction of the magnetic force $\vec{F}$ acting on it?

Accepted Answer

Upward (towards the top of the page)

Question 8

Which of the following correctly expresses Ohm's Law for a circuit with an emf $\mathcal{E}$ and total resistance $R$?

Accepted Answer

$I = \dfrac{\mathcal{E}}{R}$

Question 9

A circuit contains three resistors $R_1$, $R_2$, and $R_3$ in series. What is the total resistance $R_{total}$?

Accepted Answer

$R_{total} = R_1 + R_2 + R_3$

Question 10

A parallel plate capacitor is connected to a battery and then disconnected. If the plates are pulled apart, what happens to the voltage and stored energy?

Accepted Answer

Voltage increases, energy increases

Question 11

A wire carries a current $I$ in a uniform magnetic field $B$ perpendicular to the wire. What is the magnitude of the force per unit length on the wire?

Accepted Answer

$F/L = IB$

Question 12

Which equation gives the energy stored in a capacitor of capacitance $C$ charged to voltage $V$?

Accepted Answer

$U = \dfrac{1}{2}CV^2$

Question 13

A resistor of resistance $R$ is connected to a battery of emf $\mathcal{E}$ and internal resistance $r$. What is the current $I$ in the circuit?

Accepted Answer

$I = \dfrac{\mathcal{E}}{R + r}$

Question 14

A charged particle moves in a circle of radius $r$ in a uniform magnetic field $B$. What is the speed $v$ of the particle if its charge is $q$ and mass $m$?

Accepted Answer

$v = \dfrac{qBr}{m}$

Question 15

Which of the following is the correct expression for the electric field $E$ due to a point charge $q$ at a distance $r$?

Accepted Answer

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

Question 16

A circuit contains a battery, a resistor $R$, and a capacitor $C$ in series. What is the time constant $	au$ for charging the capacitor?

Accepted Answer

$	au = RC$

Question 17

Which equation gives the voltage across a resistor $R$ carrying current $I$?

Accepted Answer

$V = IR$

Question 18

A parallel plate capacitor has plates of area $A$ separated by distance $d$. If the space between the plates is filled with two layers of dielectric, each of thickness $d/2$ and dielectric constants $K_1$ and $K_2$, what is the equivalent capacitance $C_{eq}$?

Accepted Answer

$C_{eq} = \dfrac{2\epsilon_0 A}{d} \left( \dfrac{K_1 K_2}{K_1 + K_2} \right)$

Question 19

Which of the following is the correct form of Kirchhoff's junction rule for currents at a node?

Accepted Answer

$\sum i_{in} = \sum i_{out}$

Electrostatics and Circuits: Key Concepts, Formulas, and Problem-Solving Guide

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