current density???

Question

if inside cylindrical material magnetic induction=bR^a where b,a are constant and R is radial distance from axis of cylinder then find current density ie J (current/area) as function of R

Answer 1

J = rot H
integralS of J(r) = integralO of H = integralO H(r) [rdφ]
integralS of J(r) = integralO br^a [rdφ]
integralS of J(r) = 2πb r^(a+1)

J = d [integralS of J(r)] / dS = d [integralS of J(r)] / [2πrdr]
J = 1/[2πr] d [integralS of J(r)] / dr
J = 1/[2πr] d [2πb r^(a+1)] / dr
J = b/r dr^(a+1) / dr

Answer: J = (a+1)b r^(a-1)


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Oh, I forgot the imortant and treacherous case of a = -1.
In case a = -1 the answer is inifinitely thin current 2πb along z-axis .

Answer 2

the electrical powered modern-day Density is denoted via the vector image (J). electric powered modern-day is measured in Amps (that's comparable to can charge in step with 2nd [C/s]). the present density (that's a volume modern-day density) is measured in Amps in step with meter squared [A/m^2], because of the fact the present flows in a direction, and the section is measured ordinary/perpendicularly/orthogonally to that.

Answer 3

I don't condone outsourcing of homework (unless it's chemistry), so I'll just give you a hint regarding your problem: the solution can be rather easily found by employing the so called "Biot-Savart" rule. Look it up on Wikipedia or something...

Answer 4

challenging point. browse using google or bing. that will might help!