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A charge +Q is distributed uniformly along the z axis from

Chapter 3, Problem 44P

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QUESTION:

Problem 44P

A charge +Q is distributed uniformly along the z axis from z = −a to z = +a. Show that the electric potential at a point r is given by

for r > a.

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QUESTION:

Problem 44P

A charge +Q is distributed uniformly along the z axis from z = −a to z = +a. Show that the electric potential at a point r is given by

for r > a.

ANSWER:

Step 1 of 2

We have to find the expansion of electric potential V(r,) at a point due  charge +Q which  is distributed uniformly along the z axis from z = −a to z = +a.

We can do this by using the expansion for the potential of any localized charge distribution in powers of .

Here,

       

The integral splits into two parts

Now in the first integral  refer the diagram given below and and in the second integral so, .

But  so the integral cancels when  is odd and adds when is even .

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