Q: A $$1\ \mathrm{nC}$$ charge is placed at the bottom of an equilateral triangle. Two $$2\ \mathrm{nC}$$ charges are placed at the other two corners, and a $$-6\ \mathrm{nC}$$ charge is placed at the top. Each side is $$5.0\ \mathrm{cm}. $$What is the net force on the $$1\ \mathrm{nC}$$ charge (in component vector form)?

$$\vec{F} = (0, -7.2 \times 10$$^{-6}$$)\ \mathrm{N}$$

Question 1

Two uncharged metal spheres X and Y are in contact on insulating stands. A positively charged rod R is brought close to X (but does not touch). Y is then moved away from X. What are the final charge states of X and Y?

Accepted Answer

X is negative and Y is positive.

Question 2

When two point charges are a distance $$d$$ apart, the electric force that each one feels from the other has magnitude $$F. In $$order to make this force twice as strong, the distance would have to be changed to:

Accepted Answer

$$d/\sqrt{2}$$

Question 3

Two point charges $$Q_1$$ and $$Q_2$$ are placed as shown on a grid, with $$Q_1 to $$the left of $$Q_2. $$Point $$P is to $$the right of both. Which direction best represents the net electric field at point $$P$$ due to these two charges?

Accepted Answer

To the right

Question 4

Three equal negative point charges are placed at three corners of a square of side $$d. $$What is the direction of the net electric field at the center of the square?

Accepted Answer

Towards the empty corner

Question 5

An electron is projected into a region with a uniform electric field $$\vec{E}$$ pointing upwards. Which trajectory will the electron follow?

Accepted Answer

It will curve downward (opposite to $$\vec{E})$$

Question 6

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is:

Accepted Answer

Along a line between the lines closer to line #2 than line #1.

Question 7

An uncharged conductor has a hollow cavity inside of it. Within this cavity there is a charge of $$+10\ \mu\mathrm{C}$$ that does not touch the conductor. There are no other charges in the vicinity. Which statement about this conductor is true?

Accepted Answer

The outer surface of the conductor contains $$+10\ \mu\mathrm{C} of $$charge and the inner surface contains $$-10\ \mu\mathrm{C}.$$

Question 8

A $$1\ \mathrm{nC}$$ charge is placed at the bottom of an equilateral triangle. Two $$2\ \mathrm{nC}$$ charges are placed at the other two corners, and a $$-6\ \mathrm{nC}$$ charge is placed at the top. Each side is $$5.0\ \mathrm{cm}. $$What is the net force on the $$1\ \mathrm{nC}$$ charge (in component vector form)?

Accepted Answer

$$\vec{F} = (0, -7.2 	imes 10$$^{-6}$$)\ \mathrm{N}$$

Question 9

A uniformly charged rod of length $$L$$ lies along the $$y-$$axis. What is the $$x-$$component of the electric field at a point $$P on $$the $$x-$$axis, a distance $$x$$ from the end of the rod?

Accepted Answer

$$E_x = \frac{kQ}{x(x+L)}$$

Question 10

A conducting sphere of radius $$r_1 is $$surrounded by a concentric conducting shell of inner radius $$r_2$$ and outer radius $$r_3. If $$the electric field at a point outside the shell is $$E$$, what is the total charge on the exterior of the inner sphere?

Accepted Answer

$$Q = 4\pi\$$epsilon_0$$ r_1$^2 E$$

Question 11

What is the magnitude of the electric field $$E(r) at a $$distance $$r \u003c r_1$ from the center of a uniformly charged solid sphere of radius r_1$ and total charge Q$?

Accepted Answer

$$E(r) = \frac{1}{4\pi\$$epsilon_0$$} \frac{Qr}{r_1$^3}$$

Question 12

What is the magnitude of the electric field $$E(r) at a $$distance $$r \u003e r_1$ from the center of a uniformly charged solid sphere of radius r_1$ and total charge Q$?

Accepted Answer

$$E(r) = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{r^2$}$$

Question 13

A point charge $$q is $$placed at the center of a spherical conducting shell. The shell is initially uncharged. What is the charge induced on the inner surface of the shell?

Accepted Answer

$$-q$$

Question 14

A parallel plate capacitor is connected to a battery and then the battery is disconnected. If the plates are then pulled apart to twice their original separation, what happens to the voltage across the plates?

Accepted Answer

It doubles.

Question 15

A charged particle moves in a region where the electric field is zero but the magnetic field is nonzero. What happens to the particle?

Accepted Answer

It moves in a circle if its velocity is perpendicular to the magnetic field.

Question 16

A $$+2\ \mu\mathrm{C}$$ charge and a $$-2\ \mu\mathrm{C}$$ charge are placed $$10\ \mathrm{cm}$$ apart. What is the electric field at the midpoint between them?

Accepted Answer

Points from $$+2\ \mu\mathrm{C} to$$ $$-2\ \mu\mathrm{C}$$

Question 17

A metal sphere of radius $$R$$ carries a charge $$Q. $$What is the electric field just outside the surface of the sphere?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{R^2$}$$

Electrostatics and Electric Fields: Study Notes and Problem Guide

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