Chapter 32, Problem 023 In the figure, a parallel-plate capacitor has square pla

Question

Chapter 32, Problem 023 In the figure, a parallel-plate capacitor has square plates of edge length L - 2.2 m. A current of 2.6 A charges the capacitor, producing a uniform electric field between the plates, with E perpendicular to the plates. (a) What is the displacement current id through the region between the plates? (b) What is dE/dt in this region? (c) What is the displacement current encircled by the square dashed path of edge length d-0.60 m? (d) What is B d s around this square dashed path? 1 Edge view Top view (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

Given,

Length, L = 2.2 m

current, I = 2.6 A

permittivity constant, µo = 1.26*10-6 H/m

permeability constant, eo = 8.85*10-12 C2 /N-m2

a) the displacement current id through the region between the plates is given by

id = I = 2.6 A

b) displacement current is given by

id = eo A ( dE /dt )

( dE /dt ) = id / ( eo A) = 2.6 / (8.85*10^-12)( 2.2 )^2 = 6.07*10^10 V/m.s

c) the displacement current encircled by the square dashed path of edge length d = 0.60 is given by

id = eo A ( dE /dt )

Here A = d2

id ' = eo d2 ( dE /dt) = (8.85*10^-12)(0.6)^2 (6.07*10^10) = 0.193 A

d) b vector·ds around this square dashed path is given by

int b vector·ds = µo ( id ' + id ) = (1.26*10^-6)[ 0.193 + 2.6 ] = 3.52*10^-6 T.m

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