Question 1

A rod of length $$\ell$$ has a uniform linear charge density $$\lambda$$ and total charge $$Q. $$What is the expression for the electric field at a point $$P$$ located a distance $$a$$ from one end of the rod along its axis?

Accepted Answer

$$E = \frac{\lambda}{4\pi\$$varepsilon_0$$} \left( \frac{1}{a} - \frac{1}{a+\ell} \right)$$

Question 2

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

Accepted Answer

$$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{Qz}{(z^2$ + R^2$)^{3/2}$$}$

Question 3

Two infinite parallel sheets carry uniform surface charge densities $$+\sigma$$ and $$-\sigma. $$What is the magnitude of the electric field between the sheets?

Accepted Answer

$$E = \frac{\sigma}{\$$varepsilon_0$$}$$

Question 4

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

Accepted Answer

$$E = \frac{\sigma}{2\$$varepsilon_0$$} \left(1 - \frac{x}{\sqrt{x^2$ + R^2$}} \right)$$

Question 5

If a point $$P is $$very far from a uniformly charged rod of length $$\ell$$ ($$a \gg \ell$$), how does the electric field at $$P$$ behave?

Accepted Answer

It behaves as if all the charge were concentrated at a point: $$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{Q}{a^2$}$$

Question 6

A positive charge is uniformly distributed around a semicircle of radius $$a. $$What is the direction of the electric field at the center of curvature $$P$$?

Accepted Answer

Along the $$-y$$ direction

Question 7

A negatively charged disk is placed as shown, and a negative test charge $$q_0 is $$placed at rest at point $$P$$ above the disk. What will be the direction of motion of $$q_0$$?

Accepted Answer

Away from the disk with increasing speed

Question 8

Which of the following best describes the electric field outside two oppositely charged infinite sheets?

Accepted Answer

The electric field is zero outside the sheets.

Question 9

For a ring of charge, what is the value of the electric field at the center of the ring?

Accepted Answer

Zero, due to symmetry

Question 10

A line segment of length $$2a is $$uniformly charged with total charge $$Q$$ and lies along the $$y-$$axis from $$y = -a to$$ $$y = +a. $$What is the $$x-$$component of the electric field at a point on the $$x-$$axis a distance $$x$$ from the origin?

Accepted Answer

$$dE_x = \frac{1}{4\pi\$$varepsilon_0$$} \frac{Q}{2a} \frac{x dy}{(x^2$ + y^2$)^{3/2}$$}$

Question 11

Which of the following graphs best represents the $$z-$$component of the electric field $$E_z$$ along the axis of a dipole?

Accepted Answer

Graph 2

Question 12

A charged ring produces an electric field along its axis. At what point is this field maximum?

Accepted Answer

At $$z = R$$

Question 13

What is the electric field just above a single infinite sheet of charge with surface charge density $$\sigma$$?

Accepted Answer

$$E = \frac{\sigma}{2\$$varepsilon_0$$}$$

Question 14

Which of the following statements is true about the electric field due to a continuous charge distribution?

Accepted Answer

It is found by integrating the contributions from all infinitesimal charge elements.

Question 15

A disk of radius $$R$$ has a uniform surface charge density $$\sigma. If$$ $$x \ll R$$, what is the electric field at a point on the axis close to the disk?

Accepted Answer

$$E = \frac{\sigma}{2\$$varepsilon_0$$}$$

Electric Field Calculations for Continuous Charge Distributions

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