Two identical magnetic dipoles of magnetic moments `2Am^2` are placed at a separation of `2m` with their axes perpendicular to each other in air. The resultant magnetic field at a mid point between the dipole is

Options

A. `4sqrt5 xx 10^(-5) T`
B. `2 sqrt5 xx 10^(-5) T`
C. `4 sqrt5 xx 10^(-7) T`
D. `2 sqrt5 xx 10^(-7) T`

Answer

d

Explanation

Distance of the point where magnetic field is to be calculated is at same distance` d = 1m `from both the magnets. Since both the magnets are placed perpendicular to each other, this point will be on the axis of one of the bar magnets and perpendicular bisector of the other.
`B_(1) = mu_(0)/(4 pi) (2M)/d^(3)`
`B_(2) = mu_(0)/(4 pi) M/d^(3)`
Both the fields are perpendicular so resultant can be written as follows :
`B = sqrt(B_(1)^(2) + B_(2)^(2)) = mu_(0)/(4 pi) M/d^(3) sqrt5`
` B = 10^(-7) xx 2/((1)^(3)) sqrt5`
Hence net magnetic field is `B = 2 sqrt5 xx 10^(-7) T`
Thus , option (d) is correct.