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In Fig. , AB is a non-conducting rod. Eq...

In Fig. , AB is a non-conducting rod. Equal charges of magnitude q are fixed at various points on the rod as shown. The rod is rotated uniformly about an axis passing through O and perpendicular to its length such that linear speed at the end A or B of the rod is `3 ms^(-1)`. Magnetic field at O is

A

`(11mu_(0)q)/(12 pi)`

B

`(3mu_(0)q)/(7 pi)`

C

`(mu_(0)q)/(2 pi)`

D

`(6mu_(0)q)/(13 pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
Since the rod is a rigid body, every point has same angular velocity `u=1 rad//s`. For points at a distance of `1m, V_(1)=1m//s`
For points at a distance of 2m, `v_(2)=2m//s`
If a charge rotating in a circle constitues a current I,
`B=(mu_(0)i)/(2r)`, where `i=q/t =(qv)/(2 pi r)`
Since field due to rotation of all charge are in same direction.
`B=sum(mu_(0)qv)/(4 pi r^(2))=(mu_(0)q)/(4 pi )(1+i_1/2+1/2+1/3+1/3)`.
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