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Dear sir, Please explain the concept of magnetic moment in detail and there is a sum based on it please explain how to solve it. The sum is, An insulating rod of length l carries uniform charge q distributed on it. It is pivoted at middle point and rotated with frequency f about a fixed axis perpendicular to the rod and passing through the pivot so what is the magnetic moment of the system?

Dear sir,

Please explain the concept of magnetic moment in detail and there is a sum based on it please explain how to solve it.

The sum is,

An insulating rod of length l carries uniform charge q distributed on it. It is pivoted at middle point and rotated with frequency f about a fixed axis perpendicular to the rod and passing through the pivot so what is the magnetic moment of the system?

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

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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