Three circular concentric wires of radii a, 2a and 3a are carrying currents 3l, 2l and l in same manner. Find the magnetic field at the common centre.

Options

A. `(13mu_(0)I)/(6a)`
B. `(mu_(0)I)/(6a)`
C. `(mu_(0)I)/a`
D. None of these

Answer

a

Explanation

`B=B_(1)+B_(2)+B_(3)`
`=(mu_(0)(3l))/(2a) +(mu_(0)(2l))/(2(2a))+(mu_(0)l)/(2(3a))`
`=(3mu_(0)l)/(2a)+(mu_(0)l)/(2a)+(mu_(0)l)/(6a)`
`=(9mu_(0)l+3mu_(0)l+mu_(0)l)/(6a) =(13 mu_(0)l)/(6a)`