Two identical magnetic dipoles of magnetic moments `1*0Am^2` each are placed at a separation of `2m` with their axes perpendicular to each other. What is the resultant magnetic field at a point midway between the dipoles?

Options

A. `5xx10^-7T`
B. `sqrt5xx10^-7T`
C. `10^-7T`
D. `2xx10^-7T`

Answer

B

Explanation

As the axes are perpendicular, mid point lies on axial line of one magnet and on equatorial line of other magnet.
`:. B_1=(mu_0)/(4pi)(2M)/(d^3)=(10^-7xx2xx1)/(1^3)=2xx10^-7T`
and `B_2=(mu_0)/(4pi)(M)/(d^3)=(10^-7xx1)/(1^3)=10^-7T`.
As `B_1_|_B_2`,
`:.` Resultant field `=sqrt(B_1^2+B_2^2)=sqrt5xx10^-7T`