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.?

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Answer 1 · 2018-08-04T12:16:26

Technically, no such locus exists.

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) #