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Question

Two point charges 2C and 1C are placed at x=0 and x=6 respectively. The potential will be zero at points :
  1. x=2,2
  2. x=1,5
  3. x=4,12
  4. x=2,9

A
x=2,9
B
x=2,2
C
x=1,5
D
x=4,12
Solution
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Since the two charges are opposite, in between them there will be a point where the potential is zero
Let the point be at distance a from x=0.
We know thatV=14πϵ0r where r is the distance from the charge and the point. The total potential will be the sum of the two potentials.
From the conditions of the problem, we have
24πϵ0a14πϵ0(6a)=0
here we get a=4

Also, there will be a point on the right side of the -1C charge where potential = 0. Let that point be at a distance b from x=0.
From the conditions of the problem, we have
24πϵ0b14πϵ0(b6)=0
Here we get b=12

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