The correct option is D 109 V/μm and in the positive x−direction.
Given,
Electric potential , V=20(x2−4)
The relation between electric field intensity (E) and electric potential (V) at any point is given by,
E=−∂V∂x
Substituting the values we get,
E=−ddx[20(x2−4)−1]
⇒E=+40x(x2−4)2
when x=4 μm,
⇒E=40×4(42−4)2
⇒E=40×412×12
⇒E=+109 V/μm
It will act in positive x−direction.
Hence, option (d) is correct answer.