GATE 2016 EC (EC3) – Question 65
For the charge-density profile shown, which graphical choice best describes the resultant potential distribution?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (D) Option D in the figure
Explanation
Poisson's equation gives $V^{\prime\prime}(x)=-\rho(x)/\epsilon$. In the negative-charge region b<x<0 the potential is concave upward; in the positive-charge region 0<x<a it is concave downward.
With finite volume-charge steps, potential and its first derivative remain continuous. The intended neutral localized profile has zero exterior field and hence constant potentials outside the charged regions.
Only **D** is continuous and smoothly changes from an upward-curving segment to a downward-curving one, with flat outer regions. The other choices introduce unphysical jumps in potential.