PDA

View Full Version : electric field and gaussian surface

PinkFlamingo
May26-04, 01:27 AM
A small copper spherical BB of radius a is located at the center of a larer hollow copper spherical shell of inner radius b and outer radius R. A charge of +q is on the small BB. The hollow copper shell has zero charge on it.

a) What is the electric field within the BB (for radii r<a)?

b) What is the electric field inside the copper shell (for radii that stisfy b<r<R)

c) Draw a closed Gaussian surface within the copper of the shell. What is the total flux of the electric vector through this Gaussian surgace? This result implies that charge must lie on the inside surface of the spherical shell. What charge must reside on the inside surgface of the copper shell? Since the copper shell has a total charge of zero, what charge must reside on the outer surface of the copper shell?

Please help me!!! :yuck:

So far all I've been able to figure out is that the answer to b is 0 I think???
Doc Al
May26-04, 04:33 AM
These questions require you to know two things:
(1) The electrostatic field within a conductor is zero
(2) Gauss's Law, which relates the total electric flux through a closed surface to the charge within that surface

Can you state Gauss's Law? How do you apply it?
PinkFlamingo
May26-04, 07:20 AM
Would the answer to a AND b be 0 because they're both within the conductor?
Doc Al
May26-04, 07:29 AM
Would the answer to a AND b be 0 because they're both within the conductor?
Yes. The field within both conductors is zero.
PinkFlamingo
Jun2-04, 03:24 PM
Would the answer to c be 0 as well, since the total charge is 0, the flux must be 0 too right?
Doc Al
Jun2-04, 03:47 PM
Would the answer to c be 0 as well, since the total charge is 0, the flux must be 0 too right?
See my comments:
c) Draw a closed Gaussian surface within the copper of the shell. What is the total flux of the electric vector through this Gaussian surgace?
Since it's within a conductor, the field and flux must be zero.
This result implies that charge must lie on the inside surface of the spherical shell. What charge must reside on the inside surgface of the copper shell?
So what charge must lie on the inside surface? Remember: Total charge within the Gaussian surface must be zero.
Since the copper shell has a total charge of zero, what charge must reside on the outer surface of the copper shell?
The charge on the inner surface plus the charge on the outer surface must add to zero. Figure it out.