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Question

The potential at a point x (measured in μ m)due to some charges situated on the x-axis is given by V(x)=20(x24) volt, then electric field intensity at x=4 μm is given by

A
53 V/μm and in the negative xdirection.
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B
53 V/μm and in the positive xdirection.
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C
109 V/μm and in the negative xdirection.
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D
109 V/μm and in the positive xdirection.
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Solution

The correct option is D 109 V/μm and in the positive xdirection.
Given,

Electric potential , V=20(x24)

The relation between electric field intensity (E) and electric potential (V) at any point is given by,
E=Vx

Substituting the values we get,
E=ddx[20(x24)1]

E=+40x(x24)2

when x=4 μm,
E=40×4(424)2

E=40×412×12

E=+109 V/μm

It will act in positive xdirection.

Hence, option (d) is correct answer.

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