Q: Which equation correctly expresses the torque $\tau$ on an electric dipole with dipole moment $\vec{p}$ in a uniform external electric field $\vec{E}$?

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

Question 1

A negatively charged particle is placed between the plates of a parallel plate capacitor with a uniform electric field pointing to the right. What is the direction of the force on the particle?

Accepted Answer

To the left

Question 2

A negatively charged particle is moving to the left between the plates of a parallel plate capacitor with a uniform electric field pointing to the right. What happens to its speed?

Accepted Answer

It slows down

Question 3

Which equation correctly expresses the torque $	au$ on an electric dipole with dipole moment $\vec{p}$ in a uniform external electric field $\vec{E}$?

Accepted Answer

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

Question 4

A permanent electric dipole is placed at rest in a uniform electric field. What happens to the dipole?

Accepted Answer

It does not move but rotates to align with the field

Question 5

A permanent electric dipole is placed at rest in a nonuniform electric field where the field is stronger at the location of the negative charge. What happens to the dipole?

Accepted Answer

It moves toward the region of stronger field (leftward)

Question 6

Which of the following best describes the effect of a microwave oven on water molecules?

Accepted Answer

The oscillating electric field exerts a torque on water molecules, causing them to rotate and heat up

Question 7

What is the magnitude of the torque on an electric dipole of moment $p$ in a uniform electric field $E$ at an angle $	heta$ to the field?

Accepted Answer

$	au = pE \sin 	heta$

Question 8

Two identical electric dipoles are placed in identical uniform electric fields, but in one case the field points to the right and in the other to the left. How do the magnitudes of the torques compare?

Accepted Answer

They are equal

Question 9

Which symmetry does the electric field of an infinitely long cylindrical rod of charge possess?

Accepted Answer

Translational symmetry along the axis, rotational symmetry about the axis, and reflection symmetry in planes containing or perpendicular to the axis

Question 10

A positively charged infinite plane sheet lies in the $xz$ plane at $y=0$. Which of the following electric field directions is consistent with the symmetry of the charge distribution?

Accepted Answer

Perpendicular to the plane (along $\pm y$)

Question 11

When lightning strikes an airplane, what principle explains the distribution of charge on the airplane's surface?

Accepted Answer

Gauss's law

Question 12

Which of the following is a consequence of the symmetry of a charged infinite plane sheet?

Accepted Answer

The electric field is uniform and perpendicular to the sheet

Question 13

A metal object is placed in a microwave oven. What is the most likely physical explanation for the creation of sparks?

Accepted Answer

High concentrations of free electrons in the metal respond to the oscillating electric field, causing sparks

Question 14

Which of the following statements about the force on a negative charge in a uniform electric field is correct?

Accepted Answer

The force is in the direction opposite to the field

Question 15

A charged particle is placed at rest between the plates of a parallel plate capacitor. What determines the direction of its acceleration?

Accepted Answer

The direction of the electric force acting on the particle

Question 16

Which of the following is true about the net force on a permanent electric dipole placed in a uniform electric field?

Accepted Answer

The net force is zero, but there is a torque

Question 17

Which of the following best describes the behavior of a permanent electric dipole in a nonuniform electric field?

Accepted Answer

It experiences both a net force and a torque

Question 18

If the angle between the dipole moment $\vec{p}$ and the electric field $\vec{E}$ is $180^\circ - 	heta$, what is $\sin(180^\circ - 	heta)$?

Accepted Answer

$\sin(	heta)$

Question 19

Which of the following electric field configurations matches the symmetry of an infinitely long cylindrical rod of charge aligned with the $x$ axis?

Accepted Answer

Radial field perpendicular to the axis and uniform along the axis

Electric Fields, Dipoles, and Symmetry in Physics

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