Chapter 32, Problem 026 A capacitor with parallel circular plates of radius R =

Question

Chapter 32, Problem 026 A capacitor with parallel circular plates of radius R = 2.80 cm is discharging via a current of 11.0 A. Consider a loop of radius R/3 that is centered on the central axis between the plates. (a) How much displacement current is encircled by the loop? The maximum induced magnetic field has a magnitude of 12.0 mT. At what radius (b) inside and (c) outside the capacitor gap is the magnitude of the induced magnetic field 2.90 mT? (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

for Capacitor

Electric field E = Q/eoA

here A = pi r^2

displacemnt Current Id = eo d(phi)/dt

Id = eo *d(EA)/dt

id = eo A * dE/dt

id = eo * pi (R/3)^2 * Q/eo* (piR^2)

Id = 1/9 * dq/dt

id = 11/9

Id - = 1.222 Amps

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part B : b)

Magnetic field of Circular plate B=(1/2)*uo*eo*r*(dE/dt)

Bmax/B =R/r

12/2.9 =2.8 /r

radius inside r=0.676 cm

c)

Magneitc field outside circular Capacitor

Bmax./B =r'/R

12/2.9 =r/2.8

r = 11.58cm

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