Question

A 11.5 nC charge is at x = 0cm and a -1.4 nCcharge is at x = 4 cm .

At what point or points on the x-axis is the electric potential zero?

Express your answer using two significant figures. If there is more than one answer, give each answer separated by a comma.

Answer 1

electric potential due to any charge q at a distance of R is given by V=k*q/R

where k=coloumb's constant=9*10^9

there are three distinct regions.

region 1:

x<0

but as distance from 11.5 nC is lesser, it will have greater contribution towards potential and it can never cancel out potential due to 1.4 nC.

region 2:

0<x<4 cm

let at x=d , electric potential is zero.

hence total potential at x=d is given by:

(k*q1/d)+(k*q2/(4-d))=0

where q1=11.5 nC

q2=-1.4 nC

then k*q1/d=-k*q2/(4-d)

==>11.5/d=1.4/(4-d)

==>11.5*4-11.5*d=1.4*d

==>d=3.5659 m

region 3:

d>4 cm

let at x=d , electric potential is zero.

hence total potential at x=d is given by:

(k*q1/d)+(k*q2/(d-4))=0

where q1=11.5 nC

q2=-1.4 nC

then k*q1/d=-k*q2/(d-4)

==>11.5/d=1.4/(d-4)

==>11.5*d-11.5*4=1.4*d

==>d=4.5545 m

hence there are in total two points where potential is zero.

3.5659 m, 4.5545 m

in two significant figures, answers are:

3.6 m,4.6 m