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Hello sir, please answer my doubt on magnetic moment problem i need it urgently
first read this carefully
consider a charge moving in a circular path ...let radius of its path of radius r ...
due to its motion it a current is produced along the path ...then motion this particle
can be compared to a charged ring of radius r, circulating with some angular velocity...
magnetic moment = M = IA = I(pir2) .........................1
we have to calculate magnetic moment for rod , let mid point of rod is O ...
now consider two small elements dq of thickness dx on the rod which are at distance x from center
on both sides...
this (dq+dq) charge is moving in circle so producing current ...
total charge= 2dq
charge per unit length = q/L
dq = (q/L)dx so
total charge = (2q/L)dx .........................2
total current over 1 complete revolution (t = 2pi/w) = total charge/t = (wq/piL)dx .......3 (w = angular frequency)
area of circle = pix2 so
magnetic moment = (total current)(area)
=pix2(wq/piL)dx
dM = (wq/L)x2dx
integrating both sides
M = (wq/L) (x3/3) lim 0 to L/2
M = (wq/L)(L2/24)
M = wqL2/24
now , w = 2pif so
M = piqL2/12
this is the required result
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