Two concentric coils of 10 turns each are placed in the same plane. Their radii are 20 cm and 40 cm and carry 0.2 A and 0.3 A current respectively in opposite directions. The magnetic induction (in T) at the centre is

Options

A. `3/4mu_(0)`
B. `5/4mu_(0)`
C. `7/4mu_(0)`
D. `9/4mu_(0)`

Answer

B

Explanation

Twop coils carry currents in opposite directions, Hence net magnetic induction at the centre is
`B_("net")=(mu_(2))/(4pi).2piN[(i_(1))/(r_(1))-(i_(2))/(r_(2))]`
Given N=10 turns, `i_(1)=0.2,i_(2)=0.3`A,
`r_(1)=20cm=0.2m`
`r_(2)=0=40cm`
`B_("net")=(mu_(0))/(4pi).2pixx10[(0.2)/(0.2)-(0.3)/(0.4)]=(10mu_(0))/(2)[1-(3)/(4)]`
`=(10mu_(0))/(8)=(5mu_(0))/(4)`.