A current of `0.5` A is passed through a coil of 200 turns and radius 10 cm. Another currwent carrying coil of 250 turns and radius 15 cm is kept concentric with the first and in the same plane. What is the current through the second coil if the net magnetic induction at teh centre of the coils is zero ?

Options

A. `0.3A`
B. `0.4A`
C. `0.6A`
D. `0.8A`

Answer

C

Explanation

`I_(1)=0.5A, n_(1) =200, r_(1)=0.1m,`
`n_(2) =250, r_(2)=0.15 m, I_(2)?`
The net magnetic induction at the cente of the coils is zero. For this magnitude of `vecB_(1)` = magnitude of `vecB_(2)` and the currents in the coils must flow in the opposite directions.
`therefore (mu_(0))/(4pi) ((2pi n _(1)I_(1))/(r_(1)))=(mu_(0))/(4pi)((2pin_(2)I_(2))/(r_(2)))`
`thereforen_(1) I_(1)r_(2)=n_(2) I_(2)r_(1)`
or `(I_(2))/(I_(1))=((n_(1))/(n_(2)))((r_(2))/(r _(1))) =(200)/(250)xx (0.15)/(0.1)`
`=4/5 xx3/2 =6/5`
`therefore I_(2) =6/5 I_(1) =6/5 xx1/2 =0.6A`