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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
```
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 l ( 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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