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. `sqrt5xx10^(-7)T`
C. `10^(-7)T`
D. `2xx10^(-7)T`

Answer

b

Explanation

(b) As the axes are perpendicular, mid point lies on axial line of one magnet and on equatorial line of other magnet.
`therefore B_(1)=(mu_(0))/(4pi)(2M)/(d^(3))=(10^(-7)xx2xx1)/(1^(3))=2xx10^(-7)`
and `B_(2)=(mu_(0))/(4pi)(M)/(d^(3))=10^(-7)`
`therefore` Resultant field `=sqrt(B_(2)^(2))=sqrt5xx10^(-7)T`