Question

As a parallel-plate capacitor with circular plates 24 cm in diameter is being charged, the current density of the displacement current in the region between the plates is uniform and has a magnitude of 20 A/m2.

(a) Calculate the magnitude B of the magnetic field at a distance r = 87 mm from the axis of symmetry of this region.

(b) Calculate dE/dt in this region.

Answer 1

Step-by-step explanation:

a.)

The magnitude field

`B=(\mu _0I_(enclosed))/(2\pi r)\\\\=(\mu _0(J_ar^2))/(2\pi r)\\\\=(1)/(2)(\mu _0J_ar)\\\\(0.5)(4\pi * 10^(-7))(20A/m^2)(87* 10^(-3))\\\\=1.0933* 10^(-6)T`

b.)

The displacement current

`i_d=\epsilon_0A(dE)/(dt)`

then
`(dE)/(dt)=(i_d)/(\epsilon_0A)\\\\=(J_d)/(\epsilon_0)\\\\=(20)/(8.85* 10^(-12))\\\\=2.26* 10^(12)V/ms`