Two concentric circular coils often tums each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry currents 0.2 A and 0.3 A respectively in opposite directions. The magnetic field in tesla at the centre is

Options

A. `35mu"/"4`
B. `mu"/"80`
C. `7mu"/"80`
D. `5mu"/"4`

Answer

D

Explanation

As the two coils are concentric and in the same plane , carrying currents in opposite direction , the total magnetic field at the centre of the concentri coil is
`B=B_(1)-B_(2)=(mu_(0))/(4pi)(2piN_(1)I_(1))/(r_(l))-(mu_(0))/(4pi)(2piN_(2)l_(2))/(r_(2))`
`=(mu_(0))/(2)[(N_(1)l_(1))/(r_(1))-(N_(2)l_(2))/(r_(2))]=(mu_(0))/(2)[(10xx0.2)/(0.2)-(10xx0.3)/(0.4)]=(5mu_(0))/(4)`