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The potential at a point distant x (mesu...

The potential at a point distant x (mesured in `mum` ) due to some charges situated on the x-axis is given by `V (x)=(20)/(x^(2)-4)` V. The electric field at `x=4 mum` is given by

A

5/3 Volt / `mum` and in the `-ve` x direction

B

5/3 Volt / `mum` and in the `+ve` x direction

C

10/9 Volt / `mum` and in the `-ve` x direction

D

10/9 Volt / `mum` and in the `+ve` x direction

Text Solution

Verified by Experts

The correct Answer is:
D
`V(x)=(20)/(x^(2)-4)`
`impliesE=-(dV)/(dx)=(-d)/(dx)[20(x^(2)-4)^(-1)]=(20)/((x^(2)-4)^(2))xx(2x)`
`|E|_(x=4mum)=(20(2xx4))/((16-4)^(2))=(20)/(144)xx8=(160)/(144)=(10)/(9)V//mum`.
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