Q: What is the expression for the electric field on the axis of an electric dipole at a distance $$r$$ from its center?

$$\vec{E}_{\text{dipole}} = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{2\vec{p}}{r^3$}$$

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 from the charge.

Question 2

A water molecule is a permanent electric dipole. Which of the following statements best explains why?

Accepted Answer

The electrons spend more time near the oxygen atom, creating a separation of charge.

Question 3

The electric field at a distance $$r$$ from a point charge $$q in $$vacuum is given by which of the following equations?

Accepted Answer

$$\vec{E} = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{q}{r^2$} \hat{r}$$

Question 4

Which of the following is true about the electric field lines for a dipole?

Accepted Answer

They start on the positive charge and end on the negative charge.

Question 5

The electric dipole moment $$\vec{p} is $$defined as:

Accepted Answer

$$\vec{p} = q \vec{s}$$, pointing from the negative to the positive charge

Question 6

What is the expression for the electric field on the axis of an electric dipole at a distance $$r$$ from its center?

Accepted Answer

$$\vec{E}_{	ext{dipole}} = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{2\vec{p}}{r^3$}$$

Question 7

A charged rod of length $$L$$ has a total charge $$Q$$ distributed uniformly along its length. What is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \dfrac{Q}{L}$$

Question 8

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

Accepted Answer

Electric field lines are tangent to the electric field vector at every point.

Question 9

A parallel-plate capacitor has plates of area $$A$$ and charge $$\pm Q. $$What is the magnitude of the electric field between the plates (neglecting edge effects)?

Accepted Answer

$$E = \dfrac{Q}{\$$epsilon_0$$ A}$$

Question 10

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

Accepted Answer

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

Question 11

Which of the following best describes the electric field inside a parallel-plate capacitor (far from the edges)?

Accepted Answer

It is uniform in magnitude and direction.

Question 12

A piece of glass is uniformly charged with surface charge density $$\sigma. If $$the glass is broken into three pieces, what happens to the surface charge density of each piece?

Accepted Answer

All pieces have the same surface charge density $$\sigma.$$

Question 13

Which of the following is a correct expression for the surface charge density $$\sigma$$?

Accepted Answer

$$\sigma = \dfrac{Q}{A}$$

Question 14

A proton and an electron are placed in a uniform electric field. Which statement is correct about the forces they experience?

Accepted Answer

Both experience forces of equal magnitude but in opposite directions.

Question 15

A charged particle of mass $$m$$ and charge $$q is $$placed in a uniform electric field $$\vec{E}. $$What is its acceleration?

Accepted Answer

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

Question 16

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

Accepted Answer

It is zero at the center.

Question 17

A DNA fragment with negative charge is placed in a uniform electric field during gel electrophoresis. In which direction does it move?

Accepted Answer

Toward the positive electrode.

Question 18

Which of the following best describes the electric field produced by an infinite line of positive charge?

Accepted Answer

It points radially outward and decreases as $$1/r$$ with distance.

Question 19

If the electric field at a point is the vector sum of the fields due to all charges present, this is an example of which principle?

Accepted Answer

The superposition principle

Electric Fields and Continuous Charge Distributions

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