Question

A long cylindrical conductor of radius R carries current such that current density J(r) varies as distance ‘r’ from central axis of cylinder. If magnetic field at a distance r(r < R) from axis is B(r) = 2r3. Then current density J(r) will be given as

Answer 1

Answer:

A long cylindrical conductor of radius R carries a current i as shown in the figure. The current

density J varies across the cross-section as

, where, k is a constant. Find an expression for the magnetic field B at a distance

Answer 2

Given: magnetic field at a distance r(r < R) from axis,B(r) = 2r³

To find: Current Density = J(r)

Formula to be used here:

B(r)×2πr = μJ(r)Πr²

Put B(r) = 2r³ in above equation

2r³×2πr = μJ(r)Πr²

J(r) = (2r³×2πr) / μΠr²

J(r) =(4πr²)/μ

let K = 4Π/μ

therefore, J(r) = Kr²

Hence, current density J(r) will be Kr² where K = 4Π/μ