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Question

The current diensty in a medium is given by

J=400sinθ2π(r2+4)^arAm2

The total current and the average current density flowing through the portion of a spherical surface

r = 0.8 m, π12θπ4,02π are given, respectively, by

A
15.09 A, 12.86 Am2
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B
7.17 A, 6.88 Am2
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C
12.86 A, 9.23 Am2
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D
10.28 A, 7.56 Am2
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Solution

The correct option is B 7.17 A, 6.88 Am2
Ans : (b)

I=J.dS

= π/4θ=π122πϕ=0400sinθ2π(r2+4)sinθdθdϕ

=4002π(r2+4)r2ϕ2π0π/4π/12sin2θdθ

=400r2(r2+4)π/4π/12(1cos2θ2)dθ

=400r2(r2+4)⎜ ⎜ ⎜ ⎜(π4π12)2(sin2θ4)π/4π/12⎟ ⎟ ⎟ ⎟

= 400r2(r2+4)(π12(11/24))r=0.8

= 400×0.8×0.84.64×0.13=7.17Amp

Total area = dS = r2sinθdθdϕ

= r2π/4θ=π12sinθdθ2π

=r22π0.259r=0.8

=0.82×2π×0.259

=1.041m2

Average current = 7.171.041=6.88A/m2


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