Two identcal magnetic dipole of magnetic moment `1.0 A-m^(2)` each, placed at a separation of 2 m with their axis perpendicular to each other. The resultant magnetic field at a point midway between the dipole is

Options

A. `5xx10^(-7)T`
B. `sqrt(5)xx10^(-7)T`
C. `10^(-7)T`
D. None of these

Answer

B

Explanation

With respect to `1^(st)` magnet, P lies in end side-on position
`:. B_(1)=mu_(0)/(4pi)((2M)/d^(3))` (RHS)

With respect to `2^(nd)` magnet. P lies in broad side on position.
:. `B_(2)=mu_(0)/(4pi)(M/d^(3))` (Upward)
`B_(1)=10^(-7)xx(2xx1)/1=2xx10^(-7)T, B_(2)=B_(1)/2=10^(-7)T`
As `B_(1)` and `B_(2)` are mutually perpendicular, hence the resultant magnetic field
`B_(R)=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt((2xx10^(-7))^(2)+(10^(-7))^(2))`
`=sqrt(5)xx10^(-7)T`