[MCQ/EM-04001] EM-PROBLEM

A  charge \(-e \) is placed in vacuum at the point \( (d,0,0) \), where \(d>0\). The region \( x < 0\) is filled uniformly with a metal. Find the electric field at the point \( (\tfrac{d}{2},0,0)\). Which of the following is a correct answer.

1. \( -\dfrac{10e}{9\pi\epsilon_0d^2}(1,0,0)\)
2. \( \dfrac{10e}{9\pi\epsilon_0d^2}(1,0,0)\)
3. \(\dfrac{e}{\pi\epsilon_0d^2}(1,0,0)\)
4. \(-\dfrac{e}{\pi\epsilon_0d^2}(1,0,0)\)

CSIR June 2014