Q: Three point charges are arranged as shown: $$2.0\ \mathrm{nC} at$$ $$(0, 5.0\ \mathrm{cm})$$, $$2.0\ \mathrm{nC} at$$ $$(5.0\ \mathrm{cm}, 5.0\ \mathrm{cm})$$, $$-6.0\ \mathrm{nC} at$$ $$(2.5\ \mathrm{cm}, 5.0\ \mathrm{cm})$$, and $$1.0\ \mathrm{nC} at$$ $$(2.5\ \mathrm{cm}, 0). $$What is the force on the $$1.0\ \mathrm{nC}$$ charge at the bottom 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. A positively charged rod R is brought close to X, then Y is moved away. 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 between them is $$F. To $$make the force twice as strong, the distance must be changed to:

Accepted Answer

$$d/\sqrt{2}$$

Question 3

Two point charges $$Q_1$$ and $$Q_2$$ are placed as shown. Which arrow best represents the net electric field at point $$P$$ due to these charges?

Accepted Answer

Arrow C

Question 4

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

Accepted Answer

Arrow D

Question 5

An electron is projected into a region with a uniform electric field pointing upwards. Which trajectory will the electron follow?

Accepted Answer

Trajectory Y

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 on line #1. Where is the electric field due to these lines zero?

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. Inside the cavity is a charge of $$+10\ \mu\mathrm{C}$$ that does not touch the conductor. Which statement 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

Three point charges are arranged as shown: $$2.0\ \mathrm{nC} at$$ $$(0, 5.0\ \mathrm{cm})$$, $$2.0\ \mathrm{nC} at$$ $$(5.0\ \mathrm{cm}, 5.0\ \mathrm{cm})$$, $$-6.0\ \mathrm{nC} at$$ $$(2.5\ \mathrm{cm}, 5.0\ \mathrm{cm})$$, and $$1.0\ \mathrm{nC} at$$ $$(2.5\ \mathrm{cm}, 0). $$What is the force on the $$1.0\ \mathrm{nC}$$ charge at the bottom in component vector form?

Accepted Answer

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

Question 9

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

Accepted Answer

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

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 $$r_2 is$$ $$E$$, what is the total charge on the exterior of the inner sphere?

Accepted Answer

$$Q = 4\pi\$$epsilon_0$$ r_2$^2 E$$

Question 11

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 $$r_3 is$$ $$E$$, what is the total charge on the exterior of the shell?

Accepted Answer

$$Q = 4\pi\$$epsilon_0$$ r_3$^2 E$$

Question 12

A solid conducting ball of radius $$R$$ carries a total charge $$Q. $$What is the magnitude of the electric field $$E(r) at a $$distance $$r \u003e R$$ from the center of the ball?

Accepted Answer

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

Question 13

A solid conducting ball of radius $$R$$ carries a total charge $$Q. $$What is the magnitude of the electric field $$E(r) at a $$distance $$r \u003c R$$ from the center of the ball?

Accepted Answer

$$E(r) = 0$$

Question 14

A positively charged rod is brought near a neutral metal sphere. What happens to the charges in the sphere?

Accepted Answer

Electrons move toward the rod, leaving the far side positively charged.

Question 15

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

Accepted Answer

$$-q$$

Question 16

A charged particle is released from rest in a uniform electric field. Which statement is true about its motion?

Accepted Answer

It accelerates in the direction of the electric field if positive.

Question 17

Which of the following best describes the electric field inside a conductor in electrostatic equilibrium?

Accepted Answer

It is zero everywhere inside the conductor.

Question 18

A metal sphere is grounded and a charged rod is brought near it. What is the net charge on the sphere after the rod is removed?

Accepted Answer

It is negatively charged.

Question 19

Which of the following is true about the electric field lines for two equal but opposite point charges?

Accepted Answer

They begin on the positive charge and end on the negative charge.

Electrostatics: Electric Charge, Fields, and Conductors – Study Notes

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