Question

If a potential V is 2V at x = 1mm and is zero at x=0 and volume charge density is -106εo, constant throughout the free space region between x = 0 and x = 1mm. Calculate V at x = 0.5mm.

(a) 0.875

(b) 0.675

(c) 0.475

(d) 0.275

This question was posed to me by my college director while I was bunking the class.

My question comes from Laplacian Operator topic in division Vector Calculus of Electromagnetic Theory

Answer 1

Correct option is (d) 0.275

Explanation: Del^2(V) = -ρv/εo= +106

On integrating twice with respect to x, V = 106. (x^2/2) + C1x + C2.

Substitute the boundary conditions, x = 0, V = 0 and x = 1mm, V = 2V in V,

C1 = 1500 and C2 = 0. At x = 0.5mm, we get, V = 0.875V.