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ANKUR GUPTA Grade: 12
        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?
8 years ago

Answers : (1)

Pratham Ashish
17 Points
										

4244-1589_4788_untitled.bmp


let the charge density on rod be λ = q/l


consider a small element of rod dx at a distance x from the fixed end


 charge on it dq = λ dx


when the rod rotates  the current due to this element , di = f dq


                                                                                 = f λ dx


magnetic moment of this current  element dM = di * area


                                                                = f λ dx * ∏ x^2


total magnetic moment M = ∫ dM =


                                               = ∫0 l  f λ dx * ∏ x^2


                                                = fλ∏ ∫0( x^2 ) dx  


                                                 =  fλ∏/3 * x^3 ]0 l


                                                 =  fλ∏ l^3 /3         


λ l = q , so


         M =  f∏q l^2  /3


 


 

8 years ago
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