Two concentric rings are kept in the same plane. Number of turns in both the rings is 20. Their radii are 40 cm and 80 cm and they carry electric currents of 0.4 A and 0.6 A respectively, in mutually opposite directions. The magnitude of the magnetic field produced at their centre is ______ T.

Options

A. `4mu_(0)`
B. `2mu_(0)`
C. `mu_(0)`
D. `2.5mu_(0)`

Answer

C

Explanation

`r_(1)=40cm=0.4m`
`r_(2)=80cm=0.8m`
N = 20
`I_(1)=0.4A`
`I_(2)=0.6A`
Magnetic field due to electric current `I_(1)`,
`B_(1)=(mu_(0)NI_(1))/(2r_(1))=(mu_(0)(20)(0.4))/(2xx(0.4))=10mu_(0)T`
Magnetic field due to electric current `I_(2)`,
`B_(2)=(mu_(0)NI_(2))/(2r_(2))=(mu_(0)(20)(0.6))/(2xx(0.8))=13/4mu_(0)T`
Both the magnetic fields are in opposite direction, so resulting magnetic field,
`B=B_(1)-B_(2)=10mu_(0)-30/4mu_(0)`
`thereforeB=10/4mu_(0)T`