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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