If the resistance of the upper half of rigid loop is twice that of the lower half, the magnitude of magnetic induction at the centre is equal to

Options

A. zero
B. `(mu_(0)I)/(4a)`
C. `(mu_(0)I)/(12a)`
D. None of these

Answer

c

Explanation

`:' l_(1)R_(1)=I_(2)R_(2)`
`(l_(1))/(l_(2))=(R_(2))/(R_(1))=(R_(2))/(2R_(2))=1/2`
`:. l_(2)=2l_(1)`
and `l=l_(1)+l_(2)=l_(1)+2l_(2)=3l_(1)`
`:. l_(1)=l/3` and `l_(2)=2/3l`
`:'` Magnetic field at the centre of coil
`=(mu_(0)l_(1))/(4pia)xxpi-(mu_(0)l_(2)xxpi)/(4pia)`
`:. B=(mu_(0)pi)/(4pia) (l_(1)-l_(2)) =(mu_(0))/(4a)(l/3-2/3 l) =(mu_(0))/(4a)((-l)/3) =-(mu_(0)l)/(12a)=(mu_(0)l)/(12a)`