Question 1

A rod of length $$\ell$$ has a uniform positive charge per unit length $$\lambda$$ and a 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

$$E = \frac{kQ}{a(a+\ell)}$$

Question 2

For a uniformly charged line segment along the $$y-$$axis from $$y = -a to$$ $$y = +a$$, what is the electric field at point $$P on $$the $$x-$$axis at distance $$x$$ from the origin?

Accepted Answer

$$E_x = \frac{kQx}{(x^2$ + a^2$)^{3/2}$$}$

Question 3

Why does the $$y-$$component of the electric field vanish for a uniformly charged line segment centered at the origin?

Accepted Answer

Because the vertical components from each half cancel by symmetry

Question 4

For a point charge $$Q$$, what is the electric field at a distance $$r$$ from the charge?

Accepted Answer

$$E = \frac{kQ}{r^2$}$$

Question 5

A charge $$Q is $$uniformly distributed around a conducting ring of radius $$a. $$What is the electric field at a point $$P on $$the ring axis at a distance $$x$$ from its center?

Accepted Answer

$$E = \frac{kxQ}{(x^2$ + a^2$)^{3/2}$$}$

Question 6

What is the electric field at the center of a uniformly charged ring?

Accepted Answer

$$E = 0$$

Question 7

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

Accepted Answer

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

Question 8

For an infinite plane sheet of charge, what is the electric field at a distance $$x$$ from the sheet?

Accepted Answer

$$E = \frac{\sigma}{2\$$epsilon_0$$}$$

Question 9

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

Accepted Answer

$$E = \frac{2kQ}{\pi a^2$}$$

Question 10

If $$x \gg a$$ for a uniformly charged line segment, what does the electric field at point $$P on $$the $$x-$$axis reduce to?

Accepted Answer

$$E = \frac{kQ}{x^2$}$$

Question 11

For a charged disk, as $$R 	o \infty$$, what does the electric field at a point along the axis become?

Accepted Answer

$$E = \frac{\sigma}{2\$$epsilon_0$$}$$

Question 12

Which of the following best describes the direction of the electric field produced by a positive point charge?

Accepted Answer

Radially outward

Question 13

For a line of charge, what is the electric field at a perpendicular distance $$r$$ from the line?

Accepted Answer

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

Question 14

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

Accepted Answer

$$\lambda = \frac{Q}{\ell}$$

Question 15

In the calculation of the electric field from a continuous charge distribution, why is integration used?

Accepted Answer

To sum the contributions from all infinitesimal charge elements

Question 16

For a uniformly charged disk, what is the surface charge density $$\sigma in $$terms of total charge $$Q$$ and area $$A$$?

Accepted Answer

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

Question 17

Which scenario best illustrates the use of symmetry to simplify electric field calculations?

Accepted Answer

Calculating the field at the center of a ring of charge

Question 18

For a semicircular line of charge, which component of the electric field at the center of curvature cancels due to symmetry?

Accepted Answer

The $$x-$$component

Question 19

Which integral is used to find the electric field from a ring of charge at a point on its axis?

Accepted Answer

$$\int \frac{x \, dQ}{(x^2$ + a^2$)^{3/2}$$}$

Electric Field Due to Continuous Charge Distributions

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