An infinite line charge of uniform electric charge density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity ε and electrical conductivity σ . The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnit

Step-by-step solution

This is the problem of RC circuit where the product RC is a constant. So, due to leakage current, charge and current density will exponentially decay and will infinite time. So correct answer is A For any small element Resistance R = d r σ 2 π r l Capacitance C = ϵ 2 π r l d r Product R × C = ϵ σ = constant q = q 0 e - t σ ϵ I = d q d t = q 0 σ ϵ e - t σ ϵ Current density = I A = q 0 σ ϵ e - t σ ϵ 2 π r l j ∞ e - t σ ϵ