Two small and similar bar magnets have magnetic dipole moment of 1.0 `Am^(2)` each. They are kept in a plane in such a way that their axes are perpendicular to each other. A line drawn through the axis of one magnet passes through the centre of other magnet. If the distance between their centers is 2 m, find the magnetic field at the mid point of the line joining their centers.

Explanation

`m= 1Am^(2), d_(1) = d_(2) = 1 m, mu_(0) = 4pi xx 10^(-7) TmA^(-1), B=(?)`

The magnetic field at `d_1` distance on the axis of bar magnet,
`B_1 = (mu_0)/( 4pi ). (2m)/( d_(1)^(3) ) = (4pi xx 10^(-7) xx 2 xx 1)/( 4pi xx (1)^(3) )= 10^(-7)` T
Magnetic field at a distance `d_(2)` on equator of bar magnet is,
`B_(2) = (mu_0)/( 4pi) . (m)/( d_(2) ^(3) ) = (4pi xx 10^(-7) xx 1)/( 4pi xx (1)^(3) ) = 10^(-7)` T
The magnetic field at the mid point R of the line joining between two centres of magnets,
`B= sqrt(B_(1)^(2) + B_(2)^(2) ) = sqrt((2 xx 10^(-7) )^(2) + (10^(-7) )^(2) )`
`therefore B= sqrt((2)^(2) + (1)^(2) xx 10^(-7) ) = sqrt(5) xx 10^(-7)` T