Question

A capacitor has two parallel plates with area A separated by a distance $d$. The space between plates is filled with a material having dielectric constant $K$. The material is not a perfect insulator but has resistivity $\rho$. The capacitor is initially charged with charge of magnitude Q0 on each plate that gradually discharges by conduction through the dielectric. (a) Calculate the conduction current density $j_C(t)$ in the dielectric. (b) Show that at any instant the displacement current density in the dielectric is equal in magnitude to the conduction current density but opposite in direction, so the total current density is zero at every instant.

   A capacitor has two parallel plates with area A separated by a distance $d$. The space between plates is filled with a material having dielectric constant $K$. The material is not a perfect insulator but has resistivity $\rho$. The capacitor is initially charged with charge of magnitude Q0 on each plate that gradually discharges by conduction through the dielectric. (a) Calculate the conduction current density $j_C(t)$ in the dielectric. (b) Show that at any instant the displacement current density in the dielectric is equal in magnitude to the conduction current density but opposite in direction, so the total current density is zero at every instant.

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University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 29, Problem 64

Instant Answer

Solved by Expert Salamat Ali

12/28/2019

Step 1

So, we can write $i(t) = \frac{v(t)}{R}$, where $v(t)$ is the potential across the capacitor and $R$ is the resistance of the dielectric. Show more…

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A capacitor has two parallel plates with area A separated by a distance $d$. The space between plates is filled with a material having dielectric constant $K$. The material is not a perfect insulator but has resistivity $\rho$. The capacitor is initially charged with charge of magnitude Q0 on each plate that gradually discharges by conduction through the dielectric. (a) Calculate the conduction current density $j_C(t)$ in the dielectric. (b) Show that at any instant the displacement current density in the dielectric is equal in magnitude to the conduction current density but opposite in direction, so the total current density is zero at every instant.

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