Here,
R = 2 mm
J = 2 *10^5 A/m^2
for the current through wire between R/2 and R = J * area
the current through wire between R/2 and R = J * pi (R^2 - (R/2)^2)
the current through wire between R/2 and R = 2 *10^5 * pi * (0.002^2 - (0.002/2)^2)
the current through wire between R/2 and R = 1.885 A
the the current through wire between R/2 and R is 1.885 A
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b)
J = a r^2
J = 3 *10^11 * r^2
For the current
I = integration(J * 2pir * dr)
I = integration(3 *10^11 * 2 * pi * r^3 . dr)
I = 3 *10^11 * 2pi * [r^4/4]
I = 3 *10^11 * 2pi * [0.002^4 - 0.001^4]/4
I = 7.07 A
the current in the loop is 7.07 A
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