1. Tardigrade
  2. Question
  3. Physics
  4. 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 Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. An infinite line charge of uniform electric charge density $\lambda$. 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 $\varepsilon$ and electrical conductivity $\sigma$. 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 .

JEE AdvancedJEE Advanced 2016

Solution:

image
Electric field intensity at a distance $r(< R )$
$E=\frac{\lambda}{2 \pi \varepsilon_{0} r}$
Current density $J =\sigma E$
$J=\frac{\sigma \lambda}{2 \pi \varepsilon_{0} r}$
Due to discharging, charge density $(\lambda)$ decreases exponentially with time till it become zero. therefore answer is (D)
image