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. `4sqrt(5)xx10^(-5)` T
B. `2sqrt(5)xx10^(-5)` T
C. `4sqrt(5)xx10^(-7)` T
D. `2sqrt(5)xx10^(-7)` T

Answer

D

Explanation

Let point `P` be a midpoint between the diples. The point `P` will be in end-on position with respect to one dipole and in broad-side on position with respect to the other.
`therefore" "B_(1)=(mu_(0))/(4pi)(2m_(1))/(r_(1)^(3))=(10^(-7)xx2xx2)/((1)^(3))=4xx10^(-7)` T
and `B_(2)=(mu_(0))/(4pi)(m_(2))/(r_(2)^(3))=(10^(-7)xx2)/((1)^(3))=2xx10^(-7)` T
As `B_(1)` and `B_(2)` are perpendicular to each other, therefore the resultant magnetic field at point `P` is
`B=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt((4xx10^(-7))^(2)+(2xx10^(-7))^(2))`
`" "=10^(-7)sqrt(16+4)=10^(-7)sqrt(20)=2sqrt(5)xx10^(-7)` T