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 on the following graphs best describes the subsequent variation of the magnitude of current density j ( t ) at any point in the material .

Question

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 on the following graphs best describes the subsequent variation of the magnitude of current density j ( t ) at any point in the material . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Electric field intensity at a distance r(< R ) E=(λ/2 π ε0 r) Current density J =σ E J=(σ λ/2 π ε0 r) Due to discharging, charge density (λ) decreases exponentially with time till it become zero. therefore answer is (D)

Electric field intensity at a distance r(<R) E=2πε0​rλ​ Current density J=σE J=2πε0​rσλ​ Due to discharging, charge density (λ) decreases exponentially with time till it become zero. therefore answer is (D)

Electric field intensity at a distance $r (< R)$
$E = \frac{λ}{2 π ε _{0} r}$
Current density $J = σ E$
$J = \frac{σλ}{2 π ε _{0} r}$
Due to discharging, charge density $(λ)$ decreases exponentially with time till it become zero. therefore answer is (D)