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

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

Question 1

Which of the following statements about electric field lines is correct?

Accepted Answer

The direction of the electric field at any point is tangent to the field line at that point.

Question 2

A positive test charge is placed in an electric field. What is the direction of the force acting on it?

Accepted Answer

In the direction of the electric field.

Question 3

Which equation correctly relates the electric field $$E to $$the force $$F$$ experienced by a charge $$q$$?

Accepted Answer

$$E = \frac{F}{q}$$

Question 4

A thin ring of radius $$a$$ carries a total charge $$Q$$ uniformly distributed along its circumference. What is the magnitude of the electric field at a point $$P$$ located on the axis of the ring, a distance $$x$$ from its center?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Qx}{(x^2$ + a^2$)^{3/2}$$}$

Question 5

Which of the following best describes the electric dipole moment $$\vec{p}$$?

Accepted Answer

A vector pointing from the negative to the positive charge with magnitude $$qd.$$

Question 6

A neutral atom is placed in a uniform electric field. What happens to the atom?

Accepted Answer

It becomes polarized, developing an induced dipole moment.

Question 7

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

Accepted Answer

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

Question 8

What is the potential energy $$U of an $$electric dipole with moment $$p in a $$uniform electric field $$E at an $$angle $$	heta to $$the field?

Accepted Answer

$$U = -pE \cos	heta$$

Question 9

A thin plastic rod of length $$L$$ carries a total charge $$Q$$ uniformly distributed along its length. What is the first step to find the electric field at a point $$P a $$distance $$x$$ from the midpoint of the rod?

Accepted Answer

Divide the rod into infinitesimal elements $$dL$$ and assign each a charge $$dQ = \lambda dL.$$

Question 10

Which of the following is true about the conservation of electric charge?

Accepted Answer

The total electric charge in any region of space remains constant unless charge flows in or out.

Question 11

A disk of radius $$R$$ has a uniform surface charge density $$\sigma. $$What is the electric field at a point $$P on $$the axis of the disk, a distance $$x$$ from its center?

Accepted Answer

$$E = \frac{\sigma}{2\$$epsilon_0$$} \left(1 - \frac{x}{\sqrt{x^2$ + R^2$}}\right)$$

Question 12

If the density of electric field lines is higher in one region than another, what does this indicate?

Accepted Answer

The electric field is stronger in that region.

Question 13

A particle of charge $$q$$ and mass $$m is $$released from rest in a uniform electric field $$E. $$What is its acceleration?

Accepted Answer

$$a = \frac{qE}{m}$$

Question 14

Which of the following is a correct statement about electric field lines?

Accepted Answer

They never cross each other.

Question 15

A continuous charge distribution has a volume charge density $$\rho. $$What is the infinitesimal charge $$dQ in a $$small volume element $$dV$$?

Accepted Answer

$$dQ = \rho dV$$

Question 16

Which of the following best describes the torque on an electric dipole in a uniform electric field?

Accepted Answer

The torque tends to align the dipole with the electric field.

Question 17

A point charge $$q is $$placed in an electric field $$E. $$What is the force $$F$$ acting on the charge?

Accepted Answer

$$F = qE$$

Question 18

Which of the following is a property of electric dipoles?

Accepted Answer

They are common in polar molecules and neutral atoms in an electric field.

Question 19

A charged particle moves in a region with a constant electric field. Which of the following best describes its motion?

Accepted Answer

It accelerates uniformly in the direction of the electric field.

Electric Field and Electric Field Lines: Principles and Applications

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