The potential due to an electrostatic charge distribution is V r = q e - α r 4 π ε 0 r , where α is positive. The net charge within a sphere centred at the origin and of radius 1 / α is

Step-by-step solution

Electric field due to given charge distribution is E = - d V d r = - d d r q e - α r 4 π ε 0 r = - q 4 π ε 0 d d r e - α r r = - q 4 π ε 0 - α r e - α r - e - α r r 2 = q 4 π ε 0 · e - α r · α r + 1 r 2 Electric field at r = 1 α is E r = 1 α = q 4 π ε 0 · e - α × 1 α α × 1 α + 1 1 / α 2 = q / e 4 π ε 0 · 2 α 2 Flux through a sphere of radius 1 α is