Question

The displacement current density between the plates of a parallel-plate capacitor is uniform and has a magnitude of 19.9 A/m2 as the capacitor is being charged. What is dE/dt, the rate at which the electric field strength is changing between the plates

Answer 1

Answer:

$\dfrac{dE}{dt} \approx 2.261 \overline {36} \times 10^{12} \ V/ms$

Explanation:

The parameters given in the question are;

The magnitude of the displacement current density between the plates of a parallel-plate capacitor, J = 19.9 A/m²

We have;

$i_d = \epsilon _0 \times \dfrac{d \Phi_E}{dt} =\epsilon _0 \times A \times \dfrac{d E}{dt}$

Therefore;

$\therefore \dfrac{dE}{dt} =\dfrac{i_d}{\epsilon _0 \cdot A} =\dfrac{J}{\epsilon_0} = \dfrac{19.9}{8.8 \times 10^{-12}} \approx 2.261 \overline {36} \times 10^{12}$

Therefore;

$\therefore \dfrac{dE}{dt} \approx 2.261 \overline {36} \times 10^{12} \ V/ms$