The radii of two concentric circular coils are 8 cm and 10 cm and the number of turns in them are 40 and 10, respectively. A 5A current is passing through each of them In the direction. Determine the magnetic field produced at the centre of the two coils.

Explanation

Since current flows in the same direction through the two coils, the directions of magnetic fields at the centre due to the coils will be the same. Hence, the resultant magnetic field will be obtained by adding these magnetic fields.
For the first coil, `B_(1)=(mu_(0)M_(1)I)/(2r_(1))`
For the second coil `B_(2)=(mu_(0)N_(2)I)/(2r_(2))`
`:.` The resultant magnetic field,
`B=B_(1)+B_(2)=(mu_(0)1)/(2)((N_(1))/(r_(1))+(N_(2))/(r_(2)))`
`=(4pixx10^(-7)xx5)/(2)((40)/(8)+(10)/(10))`
`=2pixx10^(-7)xx5xx6=1.885 xx10^(-5)W,b*m^(-2)`.