A capacitor with circular plates (of radius R) is discharged at time r -0, when

Question

A capacitor with circular plates (of radius R) is discharged at time r -0, when a switch is closed and a constant flow of charge, /, is then allowed to flow onto its plates. Knowing that, from Gauss' Law, the electric field between the plates is constant and proportional to the charge density... C = epsilon 0 A/d E = sigma/ eplsion0 I walk a Semicircular path around the edge of the capacitor and then cut through the center enclosing half of the plates cross-sectional are . Evaluate the integral f B.dl for this closed path. This should be a one-line answer! What is the magnetic field strength as a function of radius, between the capacitor plates? Assume that the magnetic field has no radial component ... What is the magnitude and direction of the pointing Vector, S , as measured along the circular border of the capacitor? You may express your answer in terms of current/ and charge on the plateQ...

Explanation / Answer

a)   i(inclose) = current inclosed by semicircular =I/2

      Integration [ B*dL] = mu*i(inclose)   = mu* i/2

where mu =4pi*10^-7

b)   Integration [ B*dL] = mu*i(inclose)   = mu* i/2

         B*(pi*r + 2r) =mu* i/2

       B =mu* i/ (2 (pi*r + 2r) )

c) P = poynting vector

     P = Ex H

now E = sigma/(epsilon) = Q/(A*epsilon)

        H = B/mu = i/ (2 (pi*r + 2r) )

    

hence P = Q/(A*epsilon) x i/ (2 (pi*r + 2r) )

                = Q*i/[ 2*A*epsilon *(pi*r + 2r) ]

dircetion of P is raidally outwrad

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