Q: A point charge $$q = +3.0 \ \mu C is $$placed at the origin. What is the magnitude and direction of the electric field at a point $$0.50 \ m$$ directly to the right of the charge?

$$E = 1.08 \times 10^5$ \ N/C to $$the right

Q: What is the electric flux through a flat surface of area $$A = 2.0 \ m^2$ placed in a uniform electric field E = 500$$ \ N/C$$ at an angle $$\phi = 60^\circ$$ to the field direction?

$$\Phi_E = EA \cos \phi = 500 \times 2.0 \times \cos 60^\circ = 500 \ \text{N} \cdot \text{m}^2/\text{C}$$

Q: A parallel-plate capacitor has plates of area $$0.10 \ m^2$ separated by 2.0$$ \ mm$$ in vacuum. What is its capacitance?

$$C = \$$varepsilon_0$$ \frac{A}{d} = 8.85 \times 10$$^{-12}$$ \frac{0.10}{2.0 \times 10$$^{-3}$$} = 4.43 \times 10$$^{-10}$$ \ F$$

Question 1

A point charge $$q = +3.0 \ \mu C is $$placed at the origin. What is the magnitude and direction of the electric field at a point $$0.50 \ m$$ directly to the right of the charge?

Accepted Answer

$$E = 1.08 	imes 10^5$ \ N/C to $$the right

Question 2

Which of the following statements about electric field lines is correct?

Accepted Answer

Electric field lines always point away from positive charges and toward negative charges.

Question 3

A $$2.0 \ \mu C$$ charge is located at $$(0, 0.30 \ m)$$ and another $$2.0 \ \mu C$$ charge is at $$(0, 0). $$What is the net force on a $$4.0 \ \mu C$$ charge placed at $$(0.40 \ m, 0)$$? (Refer to the first image.)

Accepted Answer

The net force is the vector sum of the forces from both $$2.0 \ \mu C$$ charges, calculated using Coulomb's law.

Question 4

What is the electric flux through a flat surface of area $$A = 2.0 \ m^2$ placed in a uniform electric field E = 500$$ \ N/C$$ at an angle $$\phi = 60^\circ$$ to the field direction?

Accepted Answer

$$\Phi_E = EA \cos \phi = 500 	imes 2.0 	imes \cos 60^\circ = 500 \ 	ext{N} \cdot 	ext{m}^2/	ext{C}$$

Question 5

A parallel-plate capacitor has plates of area $$0.10 \ m^2$ separated by 2.0$$ \ mm$$ in vacuum. What is its capacitance?

Accepted Answer

$$C = \$$varepsilon_0$$ \frac{A}{d} = 8.85 	imes 10$$^{-12}$$ \frac{0.10}{2.0 	imes 10$$^{-3}$$} = 4.43 	imes 10$$^{-10}$$ \ F$$

Question 6

Which of the following best describes the effect of inserting a dielectric material with dielectric constant $$k$$ between the plates of a capacitor?

Accepted Answer

The capacitance increases by a factor of $$k.$$

Question 7

A $$12 \ V$$ battery is connected to a $$4 \ \Omega$$ resistor. What is the current through the resistor?

Accepted Answer

$$I = \frac{V}{R} = \frac{12}{4} = 3 \ A$$

Question 8

Which of the following is true for resistors in parallel?

Accepted Answer

They all have the same voltage across them.

Question 9

A wire of length $$L$$ and cross-sectional area $$A$$ has resistance $$R. If $$the wire is stretched to twice its original length without changing its volume, what happens to its resistance?

Accepted Answer

The resistance increases by a factor of 4.

Question 10

A $$9.0 \ V$$ battery with internal resistance $$r = 1.0 \ \Omega is $$connected to an external resistor $$R = 8.0 \ \Omega. $$What is the current in the circuit?

Accepted Answer

$$I = \frac{\varepsilon}{R + r} = \frac{9.0}{8.0 + 1.0} = 1.0 \ A$$

Question 11

Which of the following is a correct application of Kirchhoff’s junction rule?

Accepted Answer

$$I_1$$ + $$I_2$$ = $$I_3 at a $$junction where $$I_1$$ and $$I_2$$ enter and $$I_3$$ leaves.

Question 12

A $$5.0 \ \mu F$$ and a $$10.0 \ \mu F$$ capacitor are connected in series. What is their equivalent capacitance?

Accepted Answer

$$C_{eq} = \left( \frac{1}{5.0} + \frac{1}{10.0} \$$right)^{-1}$$ = 3.33 \ \mu F$$

Question 13

A $$12 \ V$$ battery is connected to a $$6 \ \Omega$$ and a $$3 \ \Omega$$ resistor in parallel. What is the total current supplied by the battery?

Accepted Answer

$$I_{total} = \frac{12}{6} + \frac{12}{3} = 2 + 4 = 6 \ A$$

Question 14

Which of the following statements about conductors in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside the conductor is zero.

Question 15

A $$2.0 \ \mu C$$ charge is moved from a point at $$V = 10 \ V to a $$point at $$V = 2 \ V. $$What is the change in electric potential energy?

Accepted Answer

$$\Delta U = q \Delta V = 2.0 	imes 10$$^{-6}$$ 	imes (2 - 10) = -1.6 	imes 10$$^{-5}$$ \ J$$

Question 16

Which of the following best describes the relationship between electric potential and electric field?

Accepted Answer

The electric field is the negative gradient of the electric potential.

Question 17

A $$10 \ \Omega$$ and a $$20 \ \Omega$$ resistor are connected in series to a $$30 \ V$$ battery. What is the voltage drop across the $$20 \ \Omega$$ resistor?

Accepted Answer

$$V_{20} = I 	imes 20 = \frac{30}{10+20} 	imes 20 = 20 \ V$$

Question 18

Which of the following is true about equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces.

Study Guide: Electric Charge, Electric Field, Electric Potential, Capacitance, and Circuits (Chapters 17–19)

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