How Does Gauss' Law Apply to the Electric Field Around a Charged Metal Ball?

[kasse]

Homework Statement

A metal ball with radius R = 0,6 m is charged with Q = 0.15 nC. Find the electrical field as function of the distance r from the center of the ball.

The Attempt at a Solution

Gauss law:

Q = e₀*E(r)*A = e₀*E(r)*4*pi*R^2

which gives

E(r) = Q / e₀*4*pi*R^2

I know that inside the ball, the field will be 0. But obviously this is not a function of r...Am I on the right track?

 

[Doc Al]

You're fine.

E(r) = 0 for r<R is perfectly acceptable as a function of r.

 

[kasse]

And outside the ball? I would expext the field to decrease with increasing r, not be constant...

 

[Doc Al]

And outside the ball? I would expext the field to decrease with increasing r, not be constant...

Right. You have that already done in your first post. (Just change R to r in your equation for E.)

 

[rajxen]

rajxen

I guess you are correct. The field inside a conductor is zero.

Homework Statement

A metal ball with radius R = 0,6 m is charged with Q = 0.15 nC. Find the electrical field as function of the distance r from the center of the ball.

The Attempt at a Solution

Gauss law:

Q = e₀*E(r)*A = e₀*E(r)*4*pi*R^2

which gives

E(r) = Q / e₀*4*pi*R^2

I know that inside the ball, the field will be 0. But obviously this is not a function of r...Am I on the right track?