Q: What is the torque $$\vec{\tau}$$ experienced by a dipole with moment $$\vec{p}_e in a $$uniform electric field $$\vec{E} ($$nineteenth image)?

$$\displaystyle \vec{\tau} = \vec{p}_e \times \vec{E}$$

Question 1

Which of the following statements best describes the distribution of electric charge in a conductor versus an insulator, as illustrated in the first image?

Accepted Answer

In a conductor, charge spreads uniformly over the surface, while in an insulator, charge remains localized at the point of charging.

Question 2

A metal sphere is charged by induction as shown in the second image. Which process is responsible for the redistribution of charge on sphere A?

Accepted Answer

Electrons are repelled from sphere A to sphere B due to the presence of a charged object, causing sphere A to become positively charged.

Question 3

According to Coulomb’s law, what is the direction of the force between two point charges $$q_1$$ and $$q_2 as $$shown in the third image?

Accepted Answer

The force acts along the line connecting the two charges, either attracting or repelling depending on their signs.

Question 4

Given the arrangement of four charges at the corners of a square (fifth image), what is the net force on a charge $$Q$$ placed at the center if the charges are arranged as shown on the left?

Accepted Answer

The net force is zero because the forces from each charge cancel due to symmetry.

Question 5

In the seventh image, three charges are placed along the x-axis. What is the correct expression for the net force on the middle charge $$q$$?

Accepted Answer

The net force is $$\displaystyle F = k_e \frac{q q_1$}{|x_q - x_{q_1$}|^2} + k_e \frac{q q_2$}{|x_q - x_{q_2$}|^2}$$, where $$x_q is $$the position of $$q.$$

Question 6

A positive charge $$q is $$placed on the x-axis between two charges $$q_1 = 20.0$ mC at x=0$ and q_2$ = -10.0 mC at$$ $$x=1 m ($$eighth image). Where should $$q be $$placed so that the net force on it is zero?

Accepted Answer

At $$x = 0.67 m.$$

Question 7

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

Accepted Answer

$$\displaystyle \vec{F}_{12} = k_e \frac{q_1$ q_2$}{|\vec{r}_{12}|^2} \hat{r}_{12}$$

Question 8

In the context of electric field lines (tenth image), which statement is true about the field lines for a positive and a negative point charge?

Accepted Answer

Field lines start at positive charges and end at negative charges.

Question 9

Which of the following best describes the electric field lines for a dipole (eleventh image)?

Accepted Answer

Field lines curve from the positive charge to the negative charge, showing attraction.

Question 10

A water molecule has a dipole moment due to its structure (fifteenth image). Which property of the molecule is responsible for its permanent dipole?

Accepted Answer

The partial charges on the hydrogen and oxygen atoms and the bond angle create a separation of charge.

Question 11

What is the torque $$\vec{	au}$$ experienced by a dipole with moment $$\vec{p}_e in a $$uniform electric field $$\vec{E} ($$nineteenth image)?

Accepted Answer

$$\displaystyle \vec{	au} = \vec{p}_e 	imes \vec{E}$$

Question 12

Which equation gives the potential energy $$U of a $$dipole in a uniform electric field $$\vec{E}$$?

Accepted Answer

$$\displaystyle U = -\vec{p}_e \cdot \vec{E}$$

Question 13

Which of the following is true about the electric field produced by a point charge $$q at $$the origin (twenty-fourth image)?

Accepted Answer

$$\displaystyle \vec{E}(\vec{r}) = k_e \frac{q}{r^2$} \hat{r}$$

Question 14

For a continuous charge distribution with volume charge density $$\rho(\vec{r})$$, what is the expression for the electric field at point $$\vec{r}$$?

Accepted Answer

$$\displaystyle \vec{E}(\vec{r}) = k_e \int \frac{\rho(\vec{r}') (\vec{r} - \vec{r}')}{|\vec{r} - \vec{r}'|^3} dV'$$

Question 15

Which of the following is the correct expression for the electric flux $$\Phi_E$$ through a flat surface of area $$A in a $$uniform electric field $$\vec{E} ($$twenty-eighth image)?

Accepted Answer

$$\displaystyle \Phi_E = \vec{E} \cdot \vec{A}$$

Question 16

According to Gauss’ law, what is the electric flux $$\Phi_E$$ through a closed surface surrounding a point charge $$q ($$thirtieth image)?

Accepted Answer

$$\displaystyle \Phi_E = \frac{q}{\$$varepsilon_0$$}$$

Question 17

Which symmetry is most appropriate for applying Gauss’ law to find the electric field produced by a uniformly charged sphere?

Accepted Answer

Spherical symmetry

Question 18

A ring of radius $$r$$ carries charge $$q. $$What is the electric field $$E(x) at a $$point $$x on $$its axis of symmetry?

Accepted Answer

$$\displaystyle E(x) = k_e \frac{q x}{(x^2$ + r^2$)^{3/2}$$}$

Electric Charge, Coulomb’s Law, and Gauss’ Law: Structured Study Notes

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