Q: Two electrons are separated by a distance $$R. $$One electron exerts an electrostatic force of $$3.5 \times 10$$^{-13}$$\ \mathrm{N} on $$the other. What is the value of $$R$$? (Use $$k = 8.99 \times 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$$ and e = 1.60$$ \times $$10^{-19}$$\ \mathrm{C}$.)

$$R = \sqrt{\dfrac{k e^2$}{F}} = 2.6 \times 10$$^{-8}$$\ \mathrm{m}$$

Q: A proton enters a uniform magnetic field of $$0.90\ \mathrm{T}$$ perpendicular to the field and has a radius of curvature of $$5.3\ \mathrm{cm}. $$What is its kinetic energy?

$$KE = \dfrac{q^2$ B^2$ r^2$}{2m} = 1.7 \times 10$$^{-14}$$\ \mathrm{J}$$

Question 1

Two electrons are separated by a distance $$R. $$One electron exerts an electrostatic force of $$3.5 	imes 10$$^{-13}$$\ \mathrm{N} on $$the other. What is the value of $$R$$? (Use $$k = 8.99 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$$ and e = 1.60$$ 	imes $$10^{-19}$$\ \mathrm{C}$.)

Accepted Answer

$$R = \sqrt{\dfrac{k e^2$}{F}} = 2.6 	imes 10$$^{-8}$$\ \mathrm{m}$$

Question 2

An electron is placed in a uniform electric field pointing upward. What is the direction of the electric force on the electron?

Accepted Answer

Down

Question 3

Two large parallel metal plates are held $$d = 2.0\ \mathrm{cm}$$ apart. One plate is at $$-30\ \mathrm{V}$$ and the other at $$+10\ \mathrm{V}. A $$dust particle of mass $$3.5 	imes 10$$^{-7}$$\ \mathrm{kg}$$ and charge $$6.0 	imes 10$$^{-11}$$\ \mathrm{C} is $$placed between the plates. What is the acceleration of the dust particle?

Accepted Answer

$$a = \dfrac{q \Delta V}{m d} = 0.34\ \mathrm{m/s^2$}$$

Question 4

Two charges $$q_1 = +2.0$$ 	imes $$10^{-9}$$\ \mathrm{C}$$ and q_2$ = -3.0 	imes 10$$^{-9}$$\ \mathrm{C}$$ are separated by $$a = 4.0\ \mathrm{cm}$$ and $$b = 1.7\ \mathrm{cm}$$ from point $$P at $$the origin. What is the electric potential at point $$P$$?

Accepted Answer

$$V = k \left( \dfrac{q_1$}{b} + \dfrac{q_2$}{\sqrt{a^2$ + b^2$}} \right) = 440\ \mathrm{V}$$

Question 5

Consider two capacitors with the same size plates. Capacitor 1 has separation $$d$$ and voltage $$V. $$Capacitor 2 has separation $$2d$$ and voltage $$2V. $$Which best describes the relative amount of charge on the plates of each capacitor?

Accepted Answer

Capacitor 1 has the same amount of charge as Capacitor 2

Question 6

A metal wire with resistivity $$2.65 	imes 10$$^{-8}$$\ \Omega\cdot\mathrm{m}$$ has a radius of $$2\ \mathrm{mm}$$ and will carry a maximum current of $$20\ \mathrm{A}. $$What is the maximum length of the wire such that the voltage drop does not exceed $$2.3\ \mathrm{V}$$?

Accepted Answer

$$\ell = \dfrac{\pi r^2$ V}{\rho I} = 55\ \mathrm{m}$$

Question 7

What is the current passing through a $$250\ \Omega$$ resistor that dissipates a power of $$6.7\ \mathrm{W}$$?

Accepted Answer

$$I = \sqrt{\dfrac{P}{R}} = 160\ \mathrm{mA}$$

Question 8

For the circuit shown in the first image, if $$\$$varepsilon_1$$ = 12\ \mathrm{V}$$, $$\$$varepsilon_2$$ = 9.0\ \mathrm{V}$$, $$R_1 = 100$$\ \Omega$$, and R_2$ = 160\ \Omega$$, what is the current flowing in the circuit?

Accepted Answer

$$I = \dfrac{\$$varepsilon_1$$ - \$$varepsilon_2$$}{R_1$ + R_2$} = 0.012\ \mathrm{A} = 12\ \mathrm{mA}$$

Question 9

Which one of the following equations is NOT correct for the circuit shown in the second image?

Accepted Answer

$$I_3$$ $$R_3$$ + $$I_4$$ $$R_4 = 0$

Question 10

Consider the two circuits shown in the third image, where $$C_1 = 2.0$$\ \mathrm{mF}$$, C_2$ = 3.0\ \mathrm{mF}$$, $$C_3 = 2.0$$\ \mathrm{mF}$$, and C_4$ = 3.0\ \mathrm{mF}. $$Which one of the following statements is true?

Accepted Answer

$$Q_1$$ = $$Q_2$$ and $$V_3$$ = $$V_4$$

Question 11

A proton enters a uniform magnetic field of $$0.90\ \mathrm{T}$$ perpendicular to the field and has a radius of curvature of $$5.3\ \mathrm{cm}. $$What is its kinetic energy?

Accepted Answer

$$KE = \dfrac{q^2$ B^2$ r^2$}{2m} = 1.7 	imes 10$$^{-14}$$\ \mathrm{J}$$

Question 12

A $$5.0\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}$$ and then disconnected from the battery. If the plates are pulled apart so the distance between them doubles, what is the new voltage across the capacitor?

Accepted Answer

$$V_{new} = 2 V_{initial} = 24\ \mathrm{V}$$

Question 13

A $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor are connected in parallel across a $$12\ \mathrm{V}$$ battery. What is the total current supplied by the battery?

Accepted Answer

$$I_{total} = \dfrac{V}{R_{eq}} = 1.8\ \mathrm{A}$$

Question 14

A $$2.0\ \mathrm{mF}$$ and a $$3.0\ \mathrm{mF}$$ capacitor are connected in series across a $$12\ \mathrm{V}$$ battery. What is the charge on each capacitor?

Accepted Answer

$$Q = C_{eq} V = 4.8 	imes 10$$^{-3}$$\ \mathrm{C}$$

Question 15

A 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

$$R_{new} = \dfrac{\rho (2L)}{A/2} = 4R$$

Question 16

A $$1.0\ \mathrm{kg}$$ object carries a charge of $$2.0 	imes 10$$^{-6}$$\ \mathrm{C}$$ and is placed in a uniform electric field of $$5.0 	imes 10^4$\ \mathrm{N/C}. $$What is the magnitude of the force on the object and its resulting acceleration?

Accepted Answer

$$F = qE = 0.10\ \mathrm{N}$$, $$a = 0.10\ \mathrm{m/s^2$}$$

Physics 1201: Midterm I Review – Circuits, Capacitors, and Electric Forces

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