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Question

Two point charges Q and −Q/4 are separated by a distance x . Then

A
potential is zero at a point on the axis which is x / 3 on the right side of the charge Q/4
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B
potential is zero at a point on the axis which is x / 5 on the left side of the charge Q/4
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C
electric field is zero at a point on the axis which is at a distance x on the right side of the charge Q/4
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D
there exist two points on the axis where electric field is zero.
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Solution

The correct options are
A potential is zero at a point on the axis which is x / 3 on the right side of the charge Q/4
B potential is zero at a point on the axis which is x / 5 on the left side of the charge Q/4
C electric field is zero at a point on the axis which is at a distance x on the right side of the charge Q/4

Vp=KQx+rKQ/4r=0

1x+r14r=0

4rxr=0

r=x3

Vp=KQ/4r+KQ(xr)=0

14r+1xr=0

r=x5



Ep=KQ(x+r)2K(Q/4)r2=0

and r>0
x=r

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