consider a lengh of 1 mt of the wire
surface area A = 2a sq.m
current flowing through the wire = I
entire current flows through the surface
current density = I/2a A/sq.m
volume of the shell dV = 2rdr
Let J = kr2 , given J grows quadratically with r
current through the shell
dI = JdV = 2kr3dr
Total current through the wire
= ka4/2
k = 2I/a4
current density J(r) = kr2 = 2Ir2/a4
consider a strip of width dr and radius r
length of the strip moving per unit time = r
charge on the strip dq= rdr
current I = dq/dt = rdr
surface current density K = rdr/dr = r
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