Two concentric coils of 20 turns each are placed in same plane. Their radii are 30 cm and 60 cma nd carry 0 . 4 A and 0 . 6 currents respectively in opposite directions. The magnetic induction at the centre in tesla is . . . . .

Options

A. `(8)/(3)mu_(0)`
B. `(2)/(3)mu_(0)`
C. `(5)/(3)mu_(0)`
D. `(10)/(3)mu_(0)`

Answer

D

Explanation

Given,
`I_(1) = 0 . 4 A` ,
`I_(2) = 0 . 6 A `
`r_(1) = 30 xx 1^(-2) m`
`r_(2) = 60 xx 10^(-2) m`
Magnetic field at O,
`B_(O) = (mu_(0))/(4pi) * 2pi [(n_(1)I_(1))/(r_(1)) - (n_(2) I_(2))/(r_(2))]`
`n_(1) = n_(2) = 20`
`B_(O)= (mu_(0))/(4pi) *2pi xx 20 [(0.4)/(30xx 10^(-2))-(0. 6)/(60 xx 10^(-2))]`
` = (mu_(0))/(2) xx 20 [ (0.8 - 0.6)/(60 xx 10 ^(-2))]`
` = (mu_(0))/(2) xx 20 xx (0 . 2)/(60 xx 10^(-2))`
` = (10)/(3) mu_(0)`