Question 1

Which of the following best describes the electric dipole moment $$\vec{p}$$ for a pair of charges $$-q$$ and $$+q$$ separated by a distance $$d$$?

Accepted Answer

$$\vec{p} = q\vec{d}$$, directed from the negative to the positive charge

Question 2

A very long, straight wire has a charge per unit length $$\lambda = 3.50 	imes 10$$^{-10}$$ \ \mathrm{C/m}. At $$what distance from the wire is the electric field magnitude equal to $$2.50 \ \mathrm{N/C}$$? (Use $$\$$epsilon_0$$ = 8.85 	imes 10$$^{-12}$$ \ \mathrm{C^2$/(N \cdot m^2$)})$$

Accepted Answer

$$r = \dfrac{\lambda}{2\pi\$$epsilon_0$$ E} = 2.51 \ \mathrm{m}$$

Question 3

Which of the following is the correct expression for the electric field at a distance $$r$$ from a point charge $$q$$?

Accepted Answer

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

Question 4

Given three negative point charges as shown in the image (two $$-5.00\ \mu\mathrm{C}$$ charges separated by $$8.00\ \mathrm{cm}$$ from a $$-2.00\ \mu\mathrm{C}$$ charge), what is the principle used to calculate the net electric field at point $$P$$?

Accepted Answer

The principle of superposition

Question 5

For a continuous line of charge with total charge $$Q$$ and length $$2a$$, what is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \dfrac{Q}{2a}$$

Question 6

Which of the following integrals correctly represents the $$x-$$component of the electric field at point $$(x,0)$$ due to a uniformly charged line of length $$2a$$ centered at the origin?

Accepted Answer

$$E_x = \dfrac{\lambda}{4\pi\$$epsilon_0$$} x \int_{-a}^{a} \dfrac{dy}{(x^2$ + y^2$)^{3/2}$$}$

Question 7

A disk has a uniform surface charge density $$\sigma. $$Which of the following best describes $$\sigma$$?

Accepted Answer

$$\sigma = \dfrac{Q}{A}$$, where $$Q is $$the total charge and $$A is $$the area

Question 8

Which of the following is the correct formula for the electric field at a point $$P$$ due to a continuous charge distribution?

Accepted Answer

$$E = \dfrac{1}{4\pi\$$epsilon_0$$} \int \dfrac{dq}{r^2$} \hat{r}$$

Question 9

For a long wire with linear charge density $$\lambda$$, what is the electric field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 10

A point $$P is $$located a distance $$y$$ above the midpoint of a line of charge of length $$2a$$ and total charge $$Q. $$What is the direction of the electric field at $$P$$?

Accepted Answer

The electric field points directly away from the line if $$Q \u003e 0$$, and toward the line if $$Q \u003c 0$$

Question 11

Which of the following is the correct definition for volumetric charge density $$\rho$$?

Accepted Answer

$$\rho = \dfrac{Q}{V}$$

Question 12

If the electric field at a point due to a charge distribution is zero, which of the following must be true?

Accepted Answer

The vector sum of all electric field contributions at that point is zero

Question 13

A line of charge has length $$2a$$ and total charge $$Q. $$What is the electric field at a point $$x on $$the $$x-$$axis, far from the line ($$x \gg a$$)?

Accepted Answer

$$E \approx \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{Q}{x^2$}$$

Question 14

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

Accepted Answer

They originate on the positive charge and terminate on the negative charge

Question 15

A charge $$q is $$distributed uniformly along a ring of radius $$R. $$What is the electric field at the center of the ring?

Accepted Answer

Zero, due to symmetry

Question 16

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

Accepted Answer

The net electric field is the vector sum of the electric fields produced by each charge

Electric Field Calculations: Discrete and Continuous Charge Distributions

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