Question

On a surface I have two point charges Qa and Qb, 1C and 4C respectivly and are placed at A(-3,0) B(3,0). Find all the points (locus) (except those that are too far away) where V=0.?

Answer 1

Technically, no such locus exists.

Explanation:

Assuming V stands for the total electric potential, then there is no answer to this question unless one of the charges is negative.

The total electric potential V at any point (x,y) is:

`V = V_a + V_b`

`" "= Q_a/r_a + Q_b/r_b`

where `r_a` and `r_b` are distance of `Q_a` and `Q_b` from the point (x,y) respectively.

Since `Q_a` and `Q_b` are both positive, V can never be zero unless `r_a` & `r_b ->oo`

Hence, there is no solution to your question unless one of the charges is negative. Then

`V = Q_a/r_a - Q_b/r_b =0`

or `- Q_a/r_a + Q_b/r_b =0`

Then you can solve the equation above for the locus by setting

`r_a= sqrt((x+3)^2+y^2)`
`r_b=sqrt((x-3)^2+y^2)`