Setting the Zero of Potential for a Charged Metal Sphere in an Electric Field

[ehrenfest]

Homework Statement

Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E_0. Explain clearly where you are setting the zero of potential.

Homework Equations

The Attempt at a Solution

If I set the 0 of the potential at the surface of the sphere (which I can do because it is at an equipotential because it is a conductor), then I don't see how the analysis is different than Example 3.8?

 

[pam]

If the sphere is at V=0, then infinity is at -Q/R.
To be consistent with other potentials, you should keep phi(infinity)=0.
Then the analysis is the same, but phi=Q/R+phi(grounded sphere).

 

[ehrenfest]

If the sphere is at V=0, then infinity is at -Q/R.

How did you get that? Did you do that in your head?

 

[genneth]

If the sphere is at V=0, then infinity is at -Q/R.
To be consistent with other potentials, you should keep phi(infinity)=0.
Then the analysis is the same, but phi=Q/R+phi(grounded sphere).

Err -- given the uniform E field, the potential at infinity is always infinite. I think ehrenfest had the right idea -- make the conductor of potential zero, and do the necessary algebra. I don't have the book, so I don't know if it reduces to some other problem in there.

 

[pam]

I meant the potential due only to the sphere, which is added to the -zE_0.
If the conducting sphere has charge Q, there will be the additional potential,
Q/R. Yes, done in my head.
But, do it your way if you want.

 

[Biest]

rethink where you set V = 0 and consider example 3.8