Two straight long conductors AOB and COD are perpendicular to each other and carry currents `I_1` and `I_2`. Find the magnitude of magnetic field induction at a point P at a distance a from the point O in a direction perpendicular to the plane ABCD

Answer

`(mu_0)/(2pia)(I_1^2+I_2^2)^(1//2)`

Explanation

Magnetic field induction at P due to current through AOB and COD will be
`B_1=(mu_0)/(4pi)(2I_1)/(a)` and `B_2=(mu_0)/(4pi)(2I_2)/(a)`
Here `vecB_1` and `vecB_2` are perpendicular to each other.
The magnitude of resultant magnetic field induction will be
`B=sqrt(B_1^2+B_2^2)=[((mu_0)/(4pi)(2I_1)/(a))^2+((mu_0)/(4pi)(2I_2)/(a))^2]^(1//2)`
`=(mu_0)/(2pia)(I_1^2+I_2^2)^(1//2)`