00:01
For part a, we want to show that qb is repelled from the sphere if qb is less than qa.
00:07
So we have to use the method of images here.
00:11
So we're going to let our image charge of qb be qb prime, and that's negative qb over 6 at a distance of r over 6.
00:20
And the image charge for qa is negative qa over 3 at a distance a prime, which is r over 3.
00:27
So the total charge on the sphere is the addition of these method charges, or negative qa plus qb over 6.
00:34
Now the force, the different forces on qb is the force due to qa, which is kqaqb over qr squared.
00:45
Now we have the force due to qa, or qa prime, which is kqa, qa, b over 3, 6r plus r over 3 squared.
00:54
And then we also have the force due to qb prime.
00:58
So our total force is kqb over r squared times all of this in the i -hat direction.
01:05
And since qb is less than qa, we see that the force is going to be repulsive.
01:13
Now for question b, we have an infinite line charge, infinite wire with a line charge density...