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# Electrical Fields in Spheres

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1) If the electric ﬁeld in some region is given (in spherical coordinates) by the expression

E(r) = (A* r(hat)+ B sin θ cos φ* φ(hat)) /r ,

where A and B are constants,

what is the charge density?

2) A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge.

(a) Find the surface charge density σ at R, at a, and at b.

(b) Find the potential at the center, using inﬁnity as the reference point.

(c) Now the outer surface is touched to a grounding wire, which lowers its potential
to zero (same as inﬁnity). How do your answers to (a) and (b) change?

3) What is the force of attraction between q and a grounded conducting sphere?

https://brainmass.com/physics/gauss-law/electrical-fields-spheres-164748

## SOLUTION This solution is FREE courtesy of BrainMass!

Hi.

Here are the solution.

The take home message here is:

The electric field inside a conductor is zero, so the potential across a conductor is constant!

Cheers and be well,

Yinon

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!