Two identical magnetic dipoles of magnetic moment `2 Am^(2)` are placed at a separation of 2 m with their axis perpendicular to each other in air. Find the resultant magnetic field at a mid-point between the dipoles.

Explanation

Magnetic field due to first dipole on the point of axis,
`B_(1) =(mu_(0))/(4pi) (2M_(1))/(r^(3)) rArr B_(1)=(10^(-7) xx 2 xx 2)/((1)^(3))`
`rArr B_(1)=4 xx 10^(-7)T`
Magnetic field due to second dipole on the point of equitorial, `B_(2)=(mu_(0))/(4pi) xx (M_(2))/(r^(3)) =(10^(-7)xx 2)/((1)^(3))`
`=2 xx 10^(-7)T`
`:.` Resultant magnetic field,
`B= sqrt(B_(1)^(2) +B_(2)^(2))`
`B=4.5 xx 10^(-7)T`