Induced charge distribution on two different radius sphere

[jemerlia]

Homework Statement

Two insulated metal spheres of equal sizes are given equal positive
charges. The two spheres are brought very close to each other without
touching. Draw the new charge distribution on the spheres if one sphere
is much larger than the other.

Homework Equations

[Coulomb's law] - qualitative result only

The Attempt at a Solution

The two spheres have different radii. Initially the charge on both spheres will be evenly distributed over their surface. The smaller sphere has the greater charge density and the more intense electic field. When the two are brought close together please confirm the charge distribution is as shown below. Perhaps there will also be separation of charge on the larger sphere. The smaller sphere will experience some charge redistribution.

N.B. The inside of the spheres are shown filled with "o" characters:

....o
...+.ooooo......+
...+.oooooooo......o.+
...+.ooooooooooo.-...+.ooo.+
...+.ooooooooooooo.-...oooooo
...+.oooooooooo.-...ooo.+
...+.oooooooo......o
...ooooo......+
...o

 

[jemerlia]

I guess it's possible the larger sphere could become a dipole if the smaller sphere was small enough and hence had a much higher charge density and hence electric field.

Is this correct?

 

[nlightner]

The larger sphere will experience a redistribution of charge, with more of the positive charges being pushed towards the side facing the smaller sphere. This is due to the repulsive force between the like charges on the two spheres. The smaller sphere will also experience a redistribution of charge, with some of the positive charges being pulled towards the larger sphere. This is due to the attractive force between the opposite charges on the two spheres. Overall, the charge distribution on the spheres will not be symmetrical, with more charge on the side facing the other sphere. This is known as induced charge distribution and is a result of the interaction between the two spheres.