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

Answer

C

Explanation

The point P is along the axis of A
Simlarly P lis along the equator of B
`therefore B_(2) =(mu_(0))/(4pi)(M)/(d^(3))=10^(-7)T`
`therefore B_(R )=10^(-7)sqrt(4+1)=sqrt(5)xx10^(-7)T`
`therefore` The magnitude of the resultant magnetic field is `5xx10^(-7)` T
Similarly P is along the equator of B
and `B_(1)` and `B_(2)` are perpendicular to each other
`B_(R )=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt(2xx10^(-7))^(2)+(10^(-7))^(2)`
`therefore` The magnitude of the resultant magnetic field is `5xx10^(-7)` T