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The potential at a point x ( measured in...

The potential at a point x ( measured in `mu` m) due to some charges situated on the x-axis is given by
`V(x)=20//(x^2-4) vol t`
the electric field at `x=4 mu m` is given by

A

`5/3 V/mu m` and in the -ve x deirection

B

`5/3 V/mu m` and in the +ve x deirection

C

`10/9 V/mu m` and in the -ve x deirection

D

`10/9 V/mu m` and in the +ve x deirection

Text Solution

Verified by Experts

The correct Answer is:
D
`V(x)=20/(x^(2)-4)`
The electric field `vec(E)` along all such lines where potential is a function of position
So `(delV)/(delx)=((x^(2)-4)(0)-20(2x))/((x^(2)-4)^(2))=(-40x)/((x^(2)-4)^(2))`
`vec(E)=(40x)/((x^(2)-4)^(2))(hat(i)) At x=4 mu m`
`vec(E)=(40(4))/((4^(2)-4)^(2))=160/144=(10/9 hat(i))V//m`
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