# Homework Help: Spheres placed in an electric field

1. May 6, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
Two neutral metal spheres of radius r and mass m each are connected by a light flexible conducting string of length L. The spheres are placed in a uniform electrostatic field E directed along the line connecting the centers of the spheres. Initially, the spheres are at rest a distance l from each other (r << l < L). Find the maximum speed v of the spheres after they are released. Neglect gravitational effects.

3. The attempt at a solution

I don't see any reason why would the spheres start moving towards each other when they are released. The question itself states that the spheres are neutral. They will not experience any electrostatic force.

2. May 6, 2014

### rude man

Well, the spheres are charge-neutral but charge will be redistributed by the E field so + charges face - charges & there is an attraction. This must happen so that the resultant E field inside the spheres is zero.

3. May 6, 2014

### rude man

Some ideas:

1. model the external E field as coming from two equal & opposite charges far away from each other.
2. use image technique to place a dipole inside the volumes occupied by the two spheres
3. calculate E directly or by E = -grad V. V(r,θ) has a pretty simple solution (polar coordinates, origin at center of each sphere).
4. since there are two spheres, use superposition to determine the net E field around the spheres by handling one sphere at a time (not sure about this last step).

4. May 6, 2014

### utkarshakash

These all seem too complex for me. I'm not aware about the image techniques you mention. Can you think of some other methods?

5. May 7, 2014

### rude man

Afraid not. There are several good discussions on image formation on the Web.
I attach one herewith.

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6. May 7, 2014

### utkarshakash

Thanks for the attachment. I will report back after I've finished reading.