Two identical magnetic dipoles a and b of magnetic moments M each, placed at a separation d with their axes perpendicular to each other. Find the magnitude of magnetic field at the point p mid way between the dipoles.

Explanation

As we know, `aP = Pb = ( d)/(2)`

`therefore ` Magnetic field at the axial point,
`B _(1) = ( mu _(0))/( 4pi) xx ( 2 M )/(( d //2) ^(3)) = ( mu_(0))/( 4pi) xx ( 16 M )/( d ^(3))`
Magnetic field at equational point,
`B _(1) = ( mu _(0))/( 4pi) xx ( 2 M )/( (d //2) ^(3)) = ( mu _(0))/( 4pi) xx ( 16 M )/( d ^(3))`
Magnetic field at equatorial point,
`B _(2) = ( mu _(0))/( 4 pi) xx ( M )/(((d)/(3)) ^(3)) = ( mu _(0))/( 4pi ) xx ( BM)/( d ^(3))`
`therefore B = sqrt ( B _(1) ^(2) + B _(2) ^(2)) = sqrt (( ( mu _(0) M xx 8)/( 4 pi d ^(3))) ^(2) (1 ^(2) + 2 ^(2)))`
`= ( mu _(0) M xx 8)/( 4 pi d ^(3)) sqrt5 = 17.88 xx (M)/( d ^(3)) xx 1 ^(-7) T`