Q: A permanent electric dipole is placed in a uniform electric field $$\vec{E}. $$What is the net force and torque on the dipole?

Net force is zero and torque is $$\vec{\tau} = \vec{p}_e \times \vec{E}.$$

Q: A water molecule has two hydrogen atoms with partial charges $$+0.3e$$ each and an oxygen atom with $$-0.6e. $$The HO bond length is $$0.96$$ Å and the bond angle is $$105^\circ. $$What is the magnitude of the dipole moment of the water molecule?

$$p_e = 2 \times 0.3e \times 0.96 \times 10$$^{-10}$$ \cos(52.5^\circ) \ \mathrm{C \cdot m}$$, where $$52.5^\circ is $$half the bond angle

Q: What is the torque $$\vec{\tau} on a $$dipole with moment $$\vec{p}_e in a $$uniform electric field $$\vec{E}$$?

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

Question 1

Which of the following best describes the direction of the electric field produced by a positive point charge?

Accepted Answer

The electric field points radially outward away from the charge.

Question 2

Given two point charges, $$q_1$$ and $$q_2$$, located at positions $$\vec{r}_1$$ and $$\vec{r}_2$$, what is the expression for the electric field at a point $$\vec{r}$$ due to both charges?

Accepted Answer

$$\vec{E}(\vec{r}) = k_e \frac{q_1$}{|\vec{r} - \vec{r}_1|^3} (\vec{r} - \vec{r}_1) + k_e \frac{q_2$}{|\vec{r} - \vec{r}_2|^3} (\vec{r} - \vec{r}_2)$$

Question 3

Which statement about electric field lines is correct?

Accepted Answer

Electric field lines never cross each other.

Question 4

A permanent electric dipole is placed in a uniform electric field $$\vec{E}. $$What is the net force and torque on the dipole?

Accepted Answer

Net force is zero and torque is $$\vec{	au} = \vec{p}_e 	imes \vec{E}.$$

Question 5

What is the potential energy $$U of a $$point charge $$q at $$position $$\vec{r} in a $$uniform electric field $$\vec{E}$$?

Accepted Answer

$$U = -q \vec{E} \cdot \vec{r}$$

Question 6

A water molecule has two hydrogen atoms with partial charges $$+0.3e$$ each and an oxygen atom with $$-0.6e. $$The HO bond length is $$0.96$$ Å and the bond angle is $$105^\circ. $$What is the magnitude of the dipole moment of the water molecule?

Accepted Answer

$$p_e = 2 	imes 0.3e 	imes 0.96 	imes 10$$^{-10}$$ \cos(52.5^\circ) \ \mathrm{C \cdot m}$$, where $$52.5^\circ is $$half the bond angle

Question 7

Why is the value of the dipole moment $$\vec{p}_e$$ independent of the choice of the origin?

Accepted Answer

Because the sum of all charges in a dipole is zero, so shifting the origin does not change $$\vec{p}_e.$$

Question 8

A charged plastic pen can pick up small neutral insulating objects like bits of paper. Which explanation is correct?

Accepted Answer

The pen induces a dipole in the paper, and the resulting attraction is due to the interaction between the charge and the induced dipole.

Question 9

What is the torque $$\vec{	au} on a $$dipole with moment $$\vec{p}_e in a $$uniform electric field $$\vec{E}$$?

Accepted Answer

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

Question 10

Which of the following statements about the superposition principle for electric fields is correct?

Accepted Answer

The net electric field at a point is the vector sum of the fields produced by each charge independently.

Question 11

A dipole with moment $$\vec{p}_e = qd \hat{z} is $$placed at the origin. What is the electric field at a point on the $$x-$$axis ($$r \gg d$$)?

Accepted Answer

$$\vec{E} = -\frac{k_e p_e}{r^3$} \hat{x}$$

Question 12

Which of the following is true about the potential energy of a dipole in a uniform electric field?

Accepted Answer

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

Question 13

Which of the following is NOT a property of electric field lines?

Accepted Answer

They can form closed loops in static fields.

Question 14

A point charge $$q is $$placed in a uniform electric field $$\vec{E}. If $$the charge is moved a distance $$\Delta \vec{r} in $$the direction of the field, what is the work done by the field?

Accepted Answer

$$W = q \vec{E} \cdot \Delta \vec{r}$$

Question 15

Why is the torque on a permanent dipole in a uniform electric field independent of the choice of the pivot point?

Accepted Answer

Because the net force on the dipole is zero, so the torque is the same about any point.

Question 16

Which of the following best explains why electrostatic interactions are weaker in media than in vacuum?

Accepted Answer

Because dipole effects in the medium reduce the effective electric field.

Question 17

A dipole with moment $$\vec{p}_e = qd \hat{z} is at $$the origin. What is the electric field at a point on the $$z-$$axis ($$r \gg d$$)?

Accepted Answer

$$\vec{E} = 2 \frac{k_e p_e}{r^3$} \hat{z}$$

Question 18

Which of the following is a correct statement about induced dipoles?

Accepted Answer

All non-polar atoms and molecules become induced dipoles in an electric field.

Electric Field and Its Effects on Point Charges and Dipoles

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