(a) Using the law of cosines, show that Eq. 3.17 can be written as follows:

where r and θ are the usual spherical polar coordinates, with the z axis along the line through q. In this form, it is obvious that V = 0 on the sphere, r = R.

(b) Find the induced surface charge on the sphere, as a function of θ. Integrate this to get the total induced charge. (What should it be?)

Reference equation 3.17

Step 1 of 4</p>

First we have to derive the given equation using data after that we need to find the induced surface charge on the sphere.

Step 2 of 4</p>

So,

Here ,

Therefore,

It is proved.

If Then