Q: Which of the following is the correct expression for the vector force on charge $$q_i$$ due to all other charges in a system?

$$\vec{F}_i = \sum_{j \neq i} k_e \frac{q_i q_j}{r_{ij}^2} \hat{r}_{ij}$$

Question 1

Which of the following statements best explains why charge distributes uniformly on the surface of a conductor but remains localized on an insulator, as shown in the first image?

Accepted Answer

In conductors, free electrons move to minimize repulsive forces, spreading charge evenly over the surface.

Question 2

A glass rod is rubbed with silk, causing the rod to become positively charged. Which process is responsible for this charging?

Accepted Answer

Friction transfers electrons from the glass rod to the silk, leaving the rod positively charged.

Question 3

Which equation correctly expresses Coulomb’s law for the force between two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r_{12}$$?

Accepted Answer

$$F = k_e \frac{q_1$ q_2$}{r_{12}^2}$$

Question 4

Given $$q_1 = 2$$ \ \mu\mathrm{C}$$ and q_2$ = -3 \ \mu\mathrm{C}$$ separated by $$0.5 \ \mathrm{m} in $$vacuum, what is the magnitude of the force between them? Use $$k_e = 8.99 	imes 10^9$ \ \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2.$$

Accepted Answer

$$F = 0.216 \ \mathrm{N}$$

Question 5

Which of the following best describes the net force on a system of two charges due to their mutual interaction?

Accepted Answer

The net force on the system is zero because the forces are equal in magnitude and opposite in direction.

Question 6

A charge $$q = 1 \ \mathrm{nC} is $$placed at the center of a square of side $$a = 1 \ \mathrm{cm}. $$Three charges are placed at the corners: $$2q at$$ $$(a, 0)$$, $$-q at$$ $$(0, a)$$, and $$q at$$ $$(a, a). $$What is the net force on the central charge?

Accepted Answer

The net force is nonzero and can be found by vector addition of the forces from each corner.

Question 7

A positive charge is placed at the center of a square with two $$+q$$ and two $$-q$$ charges at the corners (see image 5, left). What is the direction of the net force on the central charge?

Accepted Answer

The net force is zero due to symmetry.

Question 8

Which of the following materials is most likely to be a conductor?

Accepted Answer

Copper

Question 9

A charge $$q is $$placed at $$x = 6 \ \mathrm{m} on $$the x-axis, with $$q_1 = 6$$ \ \mu\mathrm{C}$$ at x = -3$$ \ \mathrm{m}$$ and q_2$ = 2 \ \mu\mathrm{C} at$$ $$x = 9 \ \mathrm{m}. $$What is the direction of the net force on $$q$$?

Accepted Answer

To the left (negative x-direction)

Question 10

A positive charge $$q is $$placed on the x-axis between $$q_1 = 20.0$$ \ \mathrm{mC}$$ at x = 0$ and q_2$ = -10.0 \ \mathrm{mC} at$$ $$x = 1.00 \ \mathrm{m}. At $$what position $$x$$ should $$q be $$placed so that the net force on it is zero?

Accepted Answer

$$x = -1.73 \ \mathrm{m}$$

Question 11

Which of the following is the correct expression for the vector force on charge $$q_i$$ due to all other charges in a system?

Accepted Answer

$$\vec{F}_i = \sum_{j 
eq i} k_e \frac{q_i q_j}{r_{ij}^2} \hat{r}_{ij}$$

Question 12

A charge $$q = -1.0 \ \mathrm{nC} is $$located at $$(0, 2) \ \mathrm{cm}$$, with $$q_1 = 2.0$$ \ \mathrm{nC}$$ at (-4$$, 0) \ \mathrm{cm}$$ and q_2$ = -3.0 \ \mathrm{nC} at$$ $$(4, 0) \ \mathrm{cm}. $$What is the direction of the net force on $$q$$?

Accepted Answer

The net force is directed downward (negative y-direction).

Question 13

Which of the following best describes the process of charging a conductor by induction, as shown in image 2?

Accepted Answer

A charged object is brought near a conductor, causing charge separation; grounding allows one type of charge to leave, leaving the conductor oppositely charged.

Question 14

Which of the following is the value of the vacuum permittivity $$\$$epsilon_0$$?

Accepted Answer

$$\$$epsilon_0$$ = 8.854 	imes 10$$^{-12}$$ \ \mathrm{C}^2/(\mathrm{N} \cdot \mathrm{m}^2)$$

Question 15

Which of the following statements about charge conservation is correct?

Accepted Answer

The net charge of all objects in a closed system remains constant during any physical process.

Question 16

Which of the following is a correct statement about the quantization of electric charge?

Accepted Answer

Electric charge exists in integer multiples of the elementary charge $$e$$ for free particles.

Question 17

A plastic ruler is rubbed with wool and becomes negatively charged. What happens to the electrons?

Accepted Answer

Electrons are transferred from the wool to the ruler.

Question 18

Which of the following best describes the force between two charges of the same sign?

Accepted Answer

The force is repulsive and acts along the line joining the charges.

Electric Charge and Coulomb’s Law: Study Notes

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