Q: Two point charges, $$q_1 = +2$$\ \mu\mathrm{C}$$ and q_2$ = -2\ \mu\mathrm{C}$$, are placed 0.5 m apart in air. What is the magnitude of the force between them?

$$F = 8.99 \times 10^9$ \frac{(2 \times 10$$^{-6}$$)(2 \times 10$$^{-6}$$)}{(0.5)^2$} = 0.144\ \mathrm{N}$$

Q: A proton is released from rest in a uniform electric field of $$E = 1.0 \times 10^4$\ \mathrm{N/C}. $$What is its acceleration?

$$a = \frac{qE}{m} = \frac{1.6 \times 10$$^{-19}$$ \times 1.0 \times 10^4$}{1.67 \times 10$$^{-27}$$} \approx 9.6 \times 10$$^{11}$$\ \mathrm{m/s^2$}$$

Q: In a circuit, a $$9\ \mathrm{V}$$ battery is connected in series with two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 4\ \Omega. $$What is the voltage drop across $$R_2$$?

$$V_2$$ = $$IR_2$$ = \frac{9}{6} \times 4 = 6\ \mathrm{V}$$

Question 1

Two point charges, $$q_1 = +2$$\ \mu\mathrm{C}$$ and q_2$ = -2\ \mu\mathrm{C}$$, are placed 0.5 m apart in air. What is the magnitude of the force between them?

Accepted Answer

$$F = 8.99 	imes 10^9$ \frac{(2 	imes 10$$^{-6}$$)(2 	imes 10$$^{-6}$$)}{(0.5)^2$} = 0.144\ \mathrm{N}$$

Question 2

A positive test charge is placed exactly midway between two equal positive charges separated by distance $$d. $$What is the direction and magnitude of the net electric field at the midpoint?

Accepted Answer

Zero; the fields from each charge cancel due to symmetry.

Question 3

Which of the following statements about electric potential $$V$$ and electric field $$E is $$correct?

Accepted Answer

The electric field is the negative gradient of the electric potential: $$\vec{E} = -
abla V.$$

Question 4

A proton is released from rest in a uniform electric field of $$E = 1.0 	imes 10^4$\ \mathrm{N/C}. $$What is its acceleration?

Accepted Answer

$$a = \frac{qE}{m} = \frac{1.6 	imes 10$$^{-19}$$ 	imes 1.0 	imes 10^4$}{1.67 	imes 10$$^{-27}$$} \approx 9.6 	imes 10$$^{11}$$\ \mathrm{m/s^2$}$$

Question 5

A copper wire of length $$L$$ and cross-sectional area $$A$$ has resistance $$R. If $$the length is doubled and the area is halved, what is the new resistance?

Accepted Answer

$$R_{new} = \rho \frac{2L}{A/2} = 4R$$

Question 6

A 12 V battery is connected to a $$6\ \Omega$$ resistor. What is the power dissipated by the resistor?

Accepted Answer

$$P = \frac{V^2$}{R} = \frac{12^2$}{6} = 24\ \mathrm{W}$$

Question 7

Three resistors, $$R_1 = 2$$\ \Omega$$, R_2$ = 3\ \Omega$$, and $$R_3 = 6$$\ \Omega$$, are connected in parallel. What is the equivalent resistance?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = 1\ \Rightarrow R_{eq} = 1\ \Omega$$

Question 8

In a circuit, a $$9\ \mathrm{V}$$ battery is connected in series with two resistors, $$R_1 = 2$$\ \Omega$$ and R_2$ = 4\ \Omega. $$What is the voltage drop across $$R_2$$?

Accepted Answer

$$V_2$$ = $$IR_2$$ = \frac{9}{6} 	imes 4 = 6\ \mathrm{V}$$

Question 9

A circuit contains a battery of emf $$\mathcal{E} = 12\ \mathrm{V}$$ and internal resistance $$r = 1\ \Omega$$, connected to an external resistor $$R = 5\ \Omega. $$What is the current in the circuit?

Accepted Answer

$$I = \frac{\mathcal{E}}{R + r} = \frac{12}{6} = 2\ \mathrm{A}$$

Question 10

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d. If $$the area is doubled and the separation is halved, how does the capacitance change?

Accepted Answer

It increases by a factor of 4: $$C = \$$varepsilon_0$$ \frac{2A}{d/2} = 4 \$$varepsilon_0$$ \frac{A}{d}$$

Question 11

A long straight wire carries a current $$I = 5\ \mathrm{A}. $$What is the magnitude of the magnetic field at a distance $$r = 0.1\ \mathrm{m}$$ from the wire?

Accepted Answer

$$B = \frac{\mu_0$ I}{2\pi r} = \frac{4\pi 	imes 10$$^{-7}$$ 	imes 5}{2\pi 	imes 0.1} = 1 	imes 10$$^{-5}$$\ \mathrm{T}$$

Question 12

A proton moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the radius of its circular path?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 13

Which of the following best explains why the magnetic force does no work on a moving charge?

Accepted Answer

Because the magnetic force is always perpendicular to the velocity, so it cannot change the speed of the particle.

Question 14

An electron moves eastward in a region where the magnetic field points upward. What is the direction of the magnetic force on the electron?

Accepted Answer

To the south (using the right-hand rule for negative charge).

Question 15

A wire of length $$L = 0.5\ \mathrm{m}$$ carries a current $$I = 3\ \mathrm{A}$$ perpendicular to a magnetic field $$B = 0.2\ \mathrm{T}. $$What is the magnitude of the force on the wire?

Accepted Answer

$$F = ILB\sin	heta = 3 	imes 0.5 	imes 0.2 = 0.3\ \mathrm{N}$$

Question 16

Which of the following is a correct statement about current in a series circuit?

Accepted Answer

The current is the same through all components.

Question 17

Why does adding more resistors in parallel always decrease the total resistance of a circuit?

Accepted Answer

Because each new path allows more current to flow, reducing the overall opposition to current.

Question 18

A charged particle moves with velocity $$\vec{v} in a $$region where both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are present. The net force is zero. What is the relationship between $$\vec{v}$$, $$\vec{E}$$, and $$\vec{B}$$?

Accepted Answer

$$\vec{E} = -\vec{v} 	imes \vec{B}$$

Question 19

A $$2\ \mu\mathrm{C}$$ charge is moved from a point where the electric potential is $$V_1 = 100$$\ \mathrm{V}$$ to a point where V_2$ = 20\ \mathrm{V}. $$What is the change in electric potential energy?

Accepted Answer

$$\Delta U = q(V_2$ - V_1$) = 2 	imes 10$$^{-6}$$ 	imes (20 - 100) = -1.6 	imes 10$$^{-4}$$\ \mathrm{J}$$

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