Question

A capacitor with parallel circular plates of radius R is discharging via a current of 12.0 A. Consider a loop of radius R/6 that is centered on the central axis between the plates. How much displacement current is encircled by the loop?

Tries 0/10

The maximum induced magnetic field has a magnitude of 38 mT. At what radial distance from the central axis of the plate is the magnitude of the induced magnetic field 15.20 mT? (enter as a fraction of R)

Answer 1

part a:

let charge on the plate be q .

area of the plates =A =pi*R^2 m^2

area of the loop=pi*(R/6)^2=A/36 m^2

given that current=12 A

==>dq/dt=12 ...(1)

electric field=E=q/(epsilon*A)

now displacement current=area of the loop*epsilon*dE/dt

=(A/36)*epsilon*(1/(epsilon*A))*dq/dt

=12/36=1/3 A

part b:

induced magnetic field varies inversely with distance.

hence if at a distance of d maximum magnetic field occurs, then if at a distance of d1 magnetic field is 15.2 mT

then 38/15.2=d1/d...(1)

now, as we know, Bmax will occur at the outer edge i.e. at a distance of R

hence d=R

Bmax=mu*I/(2*pi*R)

==>R=mu*I/(2*pi*Bmax)=4*pi*10^(-7)*12/(2*pi*0.038)=6.3158*10^(-5) m

then d1=38*d/15.2

=1.5789*10^(-4) m

hence at a distance of 2.5*R the magnetic field is 15.2 mT