## Illustration 24.3: A Cylinder of Charge

*Please wait for the animation to
completely load.*

In this animation each charge is a line or rod of charge into and
out of the screen. You can
create charge distributions and see the electric field that results **(position
is given in meters and electric field strength is given in newtons/coulomb)**.
Restart.

Begin by adding one line charge. Notice the field lines. Imagine that this
charge extends both into and out of the computer screen. Clearly, there
is cylindrical symmetry. You could imagine putting a tube centered
on this charge. How could you convince another student that the magnitude of the electric field at
any point on the tube would be the same as any other point on the tube?
Well, there is nothing special about the placement of your tube in the direction
out of the screen. There is nothing special about how long that tube is.

Now, add another line charge. What happens to the symmetry? Far away
from the two charges, there would still be cylindrical symmetry.
Why? If you are far enough away it looks (approximately) like a single
rod. Look at what happens to the field as you add 10 more line charges
and then half a
cylinder. When you create a full cylinder, what is the symmetry? The field everywhere inside the cylinder is zero.
What
Gaussian surface could you use to find the electric field inside the
cylinder or outside the cylinder? The full cylinder has cylindrical
symmetry about the middle of the cylindrical shell of line charge. Since there
is a symmetry, we can use Gauss's law to calculate the electric field.
Since there is no charge enclosed by a Gaussian surface of radius 1.65 m, the
flux is zero, and because of the symmetry we can say that E is zero inside the
cylindrical shell. We could also use a cylindrical Gaussian surface to calculate the
electric field outside of the cylindrical shell of line charge.

As you work problems using Gauss's law, you will need to be able to
identify symmetry (look at the symmetry of the charge configuration), as well
as recognize the direction of the field and where it cancels out.
Be sure that you can do that for this configuration.

Illustration authored by Anne J. Cox.

Script authored by Wolfgang Christian.

© 2004 by Prentice-Hall, Inc. A Pearson Company