Q: A glass rod is charged by rubbing with silk, acquiring a net charge of $$-3.0\ \mu\mathrm{C}. If $$its initial mass is $$12\ \mathrm{g}$$, what is the percentage change in its mass due to the loss of electrons?

$$2.4 \times 10$$^{-13}$$\ \%$$

Q: Two decorative copper balls, each of mass $$0.0240\ \mathrm{kg}$$, are placed $$45.0\ \mathrm{cm}$$ apart. How many electrons must be transferred from one ball to the other to create an attractive force of $$8000\ \mathrm{N}$$ between them? (Treat balls as point charges.)

$$2.65 \times 10$$^{15}$$ electrons

Q: You have a container with $$3.0\ \mathrm{L} of $$water at room temperature and atmospheric pressure. What is the total electrical charge of electrons in the water? (Molar mass of water $$= 18.015\ \mathrm{g/mol})$$

$$-1.6 \times 10$$^{8}$$\ \mathrm{C}$$

Q: Two charged particles are placed on the $$x-$$axis: $$q_1 = -5.0$$\ \mathrm{nC}$$ at x = 2.0$$\ \mathrm{cm}$$ and q_2$ = +10.0\ \mathrm{nC} at$$ $$x = 5.0\ \mathrm{cm}. $$What is the electric potential energy of the system?

$$-2.9 \times 10$$^{-4}$$\ \mathrm{J}$$

Q: A capacitor in a medical device stores $$300\ \mathrm{J} of $$energy in a cube-shaped region with side length $$7.0\ \mathrm{cm}$$ and dielectric constant $$110. $$What is the magnitude of the electric field between the plates?

$$4.2 \times 10$$^{3}$$\ \mathrm{V/m}$$

Question 1

Two horizontal parallel metal plates are separated by a distance $$d. $$Plate 1 acquires a uniform charge density $$\$$sigma_1$$ = +2\$$sigma_0$$ and plate 2 acquires $$\$$sigma_2$$ = -\$$sigma_0. $$What is the electric field vector at point B, midway between the plates?

Accepted Answer

$$\vec{E}_B = \frac{3\$$sigma_0$$}{2\$$varepsilon_0$$} \hat{j}$$

Question 2

Two point charges, $$q_1 = 2.0$$\ \mathrm{nC}$$ at (0$$, 2\ \mathrm{cm})$$ and q_2$ = 2.2\ \mathrm{nC} at$$ $$(0, -2\ \mathrm{cm})$$, are placed on the $$y-$$axis. What is the electric field at point $$p$$ located at $$(4\ \mathrm{cm}, 0)$$? Express your answer in components.

Accepted Answer

$$(-20\hat{i} + 9\hat{j})\ \mathrm{kN/C}$$

Question 3

A glass rod is charged by rubbing with silk, acquiring a net charge of $$-3.0\ \mu\mathrm{C}. If $$its initial mass is $$12\ \mathrm{g}$$, what is the percentage change in its mass due to the loss of electrons?

Accepted Answer

$$2.4 	imes 10$$^{-13}$$\ \%$$

Question 4

Two decorative copper balls, each of mass $$0.0240\ \mathrm{kg}$$, are placed $$45.0\ \mathrm{cm}$$ apart. How many electrons must be transferred from one ball to the other to create an attractive force of $$8000\ \mathrm{N}$$ between them? (Treat balls as point charges.)

Accepted Answer

$$2.65 	imes 10$$^{15}$$ electrons

Question 5

A dipole in a uniform external electric field $$\vec{E}$$ can be aligned such that the torque is zero. Which alignment is stable and which is unstable?

Accepted Answer

Stable when $$\vec{p}$$ and $$\vec{E}$$ are in opposite directions, unstable when $$\vec{p}$$ and $$\vec{E}$$ are in the same direction.

Question 6

You have a container with $$3.0\ \mathrm{L} of $$water at room temperature and atmospheric pressure. What is the total electrical charge of electrons in the water? (Molar mass of water $$= 18.015\ \mathrm{g/mol})$$

Accepted Answer

$$-1.6 	imes 10$$^{8}$$\ \mathrm{C}$$

Question 7

Two charged particles are placed on the $$x-$$axis: $$q_1 = -5.0$$\ \mathrm{nC}$$ at x = 2.0$$\ \mathrm{cm}$$ and q_2$ = +10.0\ \mathrm{nC} at$$ $$x = 5.0\ \mathrm{cm}. $$What is the electric potential energy of the system?

Accepted Answer

$$-2.9 	imes 10$$^{-4}$$\ \mathrm{J}$$

Question 8

A hollow conducting sphere of radius $$r_0$$ and charge $$+q$$ houses a solid conducting sphere of radius $$r_1$$ carrying charge $$-q. $$What is the potential $$V_{10} of $$the solid sphere relative to the hollow sphere? (Take potential zero at infinity.)

Accepted Answer

$$kq(1/r_0$ - 1/r_1$)$$

Question 9

A capacitor in a medical device stores $$300\ \mathrm{J} of $$energy in a cube-shaped region with side length $$7.0\ \mathrm{cm}$$ and dielectric constant $$110. $$What is the magnitude of the electric field between the plates?

Accepted Answer

$$4.2 	imes 10$$^{3}$$\ \mathrm{V/m}$$

Question 10

A stationary particle of charge $$+3.25\ \mu\mathrm{C} is at $$the origin. A second particle of charge $$-4.40\ \mu\mathrm{C}$$ moves from $$(x, y) = (-8.50\ \mathrm{cm}, 0) to$$ $$(10.0\ \mathrm{cm}, 12.5\ \mathrm{cm}). $$What is the work done by the electric force on the second particle?

Accepted Answer

$$+0.942\ \mathrm{J}$$

Question 11

Charged particles M ($$-8.50\ \mu\mathrm{C}) $$and N ($$+3.50\ \mu\mathrm{C}) $$are $$65.0\ \mathrm{cm}$$ apart. What is the electric potential at a point $$30.0\ \mathrm{cm}$$ from M, between the two charges?

Accepted Answer

$$-345\ \mathrm{kV}$$

Question 12

A plane capacitor consists of two parallel circular plates of radius $$4.0\ \mathrm{cm}$$, separated by $$0.20\ \mathrm{mm}$$, charged to $$120\ \mathrm{V}. $$Calculate (i) total energy stored and (ii) energy density within the electric field.

Accepted Answer

i) $$0.25\ \mu\mathrm{J}$$; ii) $$32\ \mathrm{J/m^3$}$$

Question 13

Two parallel plates form a capacitor with area $$12.0\ \mathrm{cm}^2$$ and separation $$12.0\ \mathrm{mm}. $$The plates are charged to a net charge of $$0.708\ \mu\mathrm{C}. (i) $$Calculate the electric field strength between the plates. (ii) Find the electric potential difference between the plates.

Accepted Answer

(i) $$66.7\ \mathrm{MV/m} (ii$$) $$80\ \mathrm{kV}$$

Question 14

A parallel-plate air capacitor has plates of $$0.200\ \mu\mathrm{C}$$ and capacitance $$300\ \mathrm{pF}$$, separated by $$0.400\ \mathrm{mm}. (i) $$Calculate the potential difference between the plates. (ii) Determine the area of each plate. (iii) Compute the magnitude of the electric field. (iv) Find the surface charge density.

Accepted Answer

i) $$667\ \mathrm{V}$$; ii) $$0.0136\ \mathrm{m}^2$$; iii) $$1.67 	imes 10^6$\ \mathrm{V/m}$$; iv) $$14.8\ \mu\mathrm{C/m}^2$$

Question 15

Determine the potential energy in electron volts (eV) of an electron-positron pair formed from a photon interaction and separated by $$0.051\ \mathrm{nm}.$$

Accepted Answer

$$-28.2\ \mathrm{eV}$$

Question 16

A device for administering electric shock operates at $$1280\ \mathrm{V}$$ and delivers a current of $$18.8\ \mathrm{mA}$$ for $$50.0\ \mathrm{ms}. $$What is the power and energy delivered per pulse?

Accepted Answer

$$24.1\ \mathrm{W};\ 1.20\ \mathrm{J}$$

Question 17

A copper pipe is $$5.0\ \mathrm{m}$$ long. The outer diameter is $$5.125$$ inches, inner diameter $$4.805$$ inches. What is the resistance of the pipe (i) along its length, (ii) along its wall thickness? Assume each area acts as an equipotential surface.

Accepted Answer

i) $$5.29 	imes 10$$^{-5}$$\ \Omega$$; ii) $$3.53 	imes 10$$^{-11}$$\ \Omega$$

Question 18

Two wires A and B have the same number of electrons flowing per unit time. Wire A has diameter $$0.8\ \mathrm{cm}$$, wire B $$1.6\ \mathrm{cm}. If $$electron drift speed in wire A is $$3.2 	imes 10$$^{-4}$$\ \mathrm{m/s}$$, what is the drift speed in wire B?

Accepted Answer

$$8.0 	imes 10$$^{-5}$$\ \mathrm{m/s}$$

Question 19

A copper power transmission cable consists of three segments with varying radii. Segments A and C have radius $$5.0\ \mathrm{cm}$$, segment B has radius $$1.67\ \mathrm{cm}. If$$ $$1000\ \mathrm{A}$$ passes through segment A, what is the current density $$J in $$each segment?

Accepted Answer

$$J_A = 1.3 	imes 10^5$\ \mathrm{A/m^2$}$$; $$J_B = 1.1 	imes 10^6$\ \mathrm{A/m^2$}$$; $$J_C = 1.3 	imes 10^5$\ \mathrm{A/m^2$}$$

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