An insulating rod of length l carries a charge q distributed uniformly on it.The rod is pivoted at an end and is rotated at a frequency f about a fixed perpendicular axis.The magnetic moment of the system is?

Question

Pratham Ashish · Answer

let the charge density on rod be &lambda; = q/l consider a small element of rod dx at a distance x from the fixed end charge on it dq = &lambda; dx when the rod rotates the current due to this element , di = f dq = f &lambda; dx magnetic moment of this current element dM = di * area = f &lambda; dx * &prod; x^2 total magnetic moment M = &int; dM = = &int; 0 l f &lambda; dx * &prod; x^2 = f&lambda;&prod; &int; 0 l ( x^2 ) dx = f&lambda;&prod;/3 * x^3 ] 0 l = f&lambda;&prod; l^3 /3 &lambda; l = q , so M = f&prod;q l^2 /3

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An insulating rod of length l carries a charge q distributed uniformly on it.The rod is pivoted at an end and is rotated at a frequency f about a fixed perpendicular axis.The magnetic moment of the system is?

An insulating rod of length l carries a charge q distributed uniformly on it.The rod is pivoted at an end and is rotated at a frequency f about a fixed perpendicular axis.The magnetic moment of the system is?

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