Question 1

A thin plastic rod of length $$a$$ carries a total charge $$+Q$$ distributed uniformly along its length. What is the linear charge density $$\lambda of $$the rod?

Accepted Answer

$$\lambda = \dfrac{Q}{a}$$

Question 2

A point $$P is $$located a distance $$d$$ from the origin on the positive $$y-$$axis, near a uniformly charged rod of length $$a$$ lying along the $$x-$$axis. What is the infinitesimal charge $$dQ on a $$segment $$dy of $$the rod?

Accepted Answer

$$dQ = \lambda dy$$

Question 3

Given a uniformly charged rod of length $$a$$ and total charge $$Q$$, what is the magnitude of the electric field $$dE at $$point $$P ($$distance $$d$$ from the origin) due to an infinitesimal segment $$dy at $$position $$y$$?

Accepted Answer

$$dE = k \dfrac{Q}{a} \dfrac{dy}{y^2$ + d^2$}$$

Question 4

A spherical shell of inner radius $$a$$ and outer radius $$b$$ carries a total charge $$+Q$$ distributed uniformly throughout its volume. What is the volume charge density $$\rho of $$the shell?

Accepted Answer

$$\rho = \dfrac{3Q}{4\pi (b^3$ - a^3$)}$$

Question 5

What is the electric field (magnitude and direction) at a distance $$r$$ from the center of a uniformly charged spherical shell, where $$r \u003c a ($$inside the inner radius)?

Accepted Answer

$$E = 0$$, directed radially

Question 6

A point charge $$q_1 is $$fixed at $$(0, 0.09\ \mathrm{m})$$ and a point charge $$q_2 is $$fixed at $$(0.09\ \mathrm{m}, 0). A $$third charge $$q_3 is $$placed at $$(0, 0). If $$the net force on $$q_3 is $$vertical, what must be true about the signs of $$q_1$$ and $$q_2$$?

Accepted Answer

$$q_1 is $$positive and $$q_2 is $$negative

Question 7

A conducting spherical shell of radius $$a$$ carries a total charge $$Q. $$What is the surface charge density $$\sigma on $$the shell?

Accepted Answer

$$\sigma = \dfrac{Q}{4\pi a^2$}$$

Question 8

A charge $$q_1 = 3.0$$ 	imes $$10^{-6}$$\ \mathrm{C}$$ is fixed at x = -0.03$$\ \mathrm{m}$$ and a charge q_2$ = -3.0 	imes 10$$^{-6}$$\ \mathrm{C} is $$fixed at $$x = +0.03\ \mathrm{m}. $$What is the electric potential at the origin ($$x = 0) $$due to both charges?

Accepted Answer

$$V = 0$$

Question 9

If the electric field at a point is zero, what can you conclude about the electric potential at that point?

Accepted Answer

The electric potential may be constant, but it is not necessarily zero.

Question 10

A charge $$q is $$released from rest at a point where the electric potential is $$V_i$$ and moves to a point where the potential is $$V_f. $$What is the change in kinetic energy $$\Delta K of $$the charge?

Accepted Answer

$$\Delta K = q(V_i - V_f)$$

Question 11

A thin rod of length $$a$$ and total charge $$Q is $$placed along the $$y-$$axis. To find the $$y-$$component of the electric field at a point $$P on $$the $$x-$$axis, which trigonometric function is needed in the integral?

Accepted Answer

$$\sin(	heta)$$

Question 12

A spherical shell of inner radius $$a$$ and outer radius $$b$$ has a total charge $$Q$$ distributed uniformly throughout its volume. What is the electric field at a distance $$r$$ from the center, where $$a \u003c r \u003c b$$?

Accepted Answer

$$E = \dfrac{Q}{4\pi\$$epsilon_0$$} \dfrac{r^3$ - a^3$}{r^2$ (b^3$ - a^3$)}$$

Question 13

Two point charges, $$q_1$$ and $$q_2$$, are placed symmetrically along the $$x-$$axis at $$x = -d$$ and $$x = +d. A $$third charge $$q_3 is $$placed at the origin. If $$q_1$$ = $$q_2$$ and $$q_3 is $$negative, what is the direction of the net force on $$q_3$$?

Accepted Answer

Along the $$x-$$axis

Question 14

A point $$P is $$located a distance $$d$$ from the origin on the $$y-$$axis, near a uniformly charged rod of length $$a on $$the $$x-$$axis. What is the correct integral expression for the $$y-$$component of the electric field at $$P$$?

Accepted Answer

$$E_y = kQ \$$int_0$$^a \dfrac{d}{(y^2$ + d^2$)^{3/2}$$} dy$

Question 15

A conducting spherical shell of radius $$a is $$surrounded by a concentric insulating shell with inner radius $$a$$ and outer radius $$b. $$The conducting shell has charge $$Q$$, and the insulating shell has charge $$-Q. $$What is the electric field at a distance $$r$$ where $$r \u003e b$$?

Accepted Answer

$$E = 0$$

Question 16

A charge $$q is $$released from rest at a point where the electric potential is $$V_i$$ and moves to a point where the potential is $$V_f. If$$ $$q is $$positive and $$V_f \u003c V_i$$, what happens to the kinetic energy of the charge?

Accepted Answer

It increases

Question 17

A thin rod of length $$a$$ and total charge $$Q is $$placed along the $$y-$$axis. What is the correct expression for the $$y-$$component of the electric field at a point $$P on $$the $$x-$$axis, distance $$d$$ from the origin?

Accepted Answer

$$E_y = \dfrac{kQd}{a} \$$int_0$$^a \dfrac{dy}{(y^2$ + d^2$)^{3/2}$$}$

Electrostatics: Forces, Fields, and Potentials – Study Notes

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