Q: A dipole consists of charges $$+q$$ and $$-q$$ separated by a distance $$s. $$What is the expression for the electric field on the axis of the dipole at a distance $$r \gg s$$ from the center?

$$E_{\text{dipole}} = \frac{1}{4\pi\$$epsilon_0$$} \frac{2p}{r^3$}$$, where $$p = qs$$

Question 1

Which of the following correctly 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

A long, straight wire carries a uniform linear charge density $$\lambda. $$What is the magnitude of the electric field a distance $$r$$ from the wire?

Accepted Answer

$$E = \frac{\lambda}{2\pi\$$epsilon_0$$ r}$$

Question 3

Which of the following statements about the electric field inside a uniformly charged spherical shell is correct?

Accepted Answer

The electric field is zero everywhere inside the shell.

Question 4

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

Accepted Answer

$$E_z = \frac{1}{4\pi\$$epsilon_0$$} \frac{Qz}{(z^2$ + R^2$)^{3/2}$$}$

Question 5

Which of the following best describes the electric field between two large, parallel, oppositely charged plates (an ideal parallel-plate capacitor)?

Accepted Answer

The electric field is uniform and points from the positive plate to the negative plate.

Question 6

A disk of radius $$R$$ carries a uniform surface charge density $$\eta. $$What happens to the electric field along the axis as $$R 	o \infty ($$the disk becomes an infinite plane)?

Accepted Answer

The electric field approaches $$E = \frac{\eta}{2\$$epsilon_0$$}$$ and becomes independent of distance from the plane.

Question 7

A dipole consists of charges $$+q$$ and $$-q$$ separated by a distance $$s. $$What is the expression for the electric field on the axis of the dipole at a distance $$r \gg s$$ from the center?

Accepted Answer

$$E_{	ext{dipole}} = \frac{1}{4\pi\$$epsilon_0$$} \frac{2p}{r^3$}$$, where $$p = qs$$

Question 8

A proton is placed very far from a uniformly charged wire. If the wire is shrunk to one-third its original length while keeping the total charge the same, what happens to the force on the proton?

Accepted Answer

The force increases by a factor of 3.

Question 9

Which of the following is true about the electric field at the center of a ring of charge?

Accepted Answer

The electric field is zero due to symmetry.

Question 10

A uniformly charged solid sphere of radius $$R$$ has total charge $$Q. $$What is the electric field at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Qr}{R^3$}$$

Question 11

A negative electron is released from rest near the center of a parallel-plate capacitor. What is its motion?

Accepted Answer

It moves with constant acceleration toward the positive plate.

Question 12

Which of the following best describes the superposition principle for electric fields?

Accepted Answer

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

Question 13

For a continuous charge distribution, how is the total electric field at a point calculated?

Accepted Answer

By integrating the electric field contributions from each infinitesimal charge element.

Question 14

A uniformly charged disk of radius $$R$$ has total charge $$Q. $$What happens to the electric field on the axis as $$z 	o 0 ($$very close to the disk)?

Accepted Answer

It approaches $$E = \frac{\eta}{2\$$epsilon_0$$}$$, where $$\eta = Q/(\pi R^2$).$$

Question 15

Which of the following is the correct expression for the electric field outside a uniformly charged sphere of radius $$R$$ and total charge $$Q$$?

Accepted Answer

$$E = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{r^2$}$$ for $$r \u003e R$$

Question 16

A parallel-plate capacitor is charged so that the left plate has charge $$+Q$$ and the right plate has charge $$-Q. $$What is the direction of the electric field inside the capacitor?

Accepted Answer

From the left plate to the right plate.

Question 17

Which of the following is a correct limiting case for the electric field of a dipole at a point far from the dipole ($$r \gg s$$)?

Accepted Answer

$$E \propto \frac{1}{r^3$}$$

Question 18

A charged ring of radius $$R$$ produces an electric field along its axis. At what point along the axis is the field zero?

Accepted Answer

At the center of the ring ($$z = 0)$$

Question 19

Which of the following best describes the electric field due to an infinite plane of charge with surface charge density $$\eta$$?

Accepted Answer

$$E = \frac{\eta}{2\$$epsilon_0$$}$$, independent of distance from the plane

Electric Fields: Point Charges, Continuous Distributions, and Applications Ch 23

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