Question

(a)State Biot-Savart’s law and express this law in the vector form. (b)Two identical circular coils ,P and Q each of radius R ,carrying currents 1 A and 3 A respectively , are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils

Answer 1

The Biot-Savart Law is an equation that describes the magnetic field created by a current-carrying wire and allows you to calculate its strength at various points. ... If you point your thumb in the direction of the current in a wire, your fingers will curl around that wire in the direction of the magnetic field

and

Two identical circular coils , P and Q each of radius is r , carrying current 1A and √3A respectively are placed vertically and perpendicular to each other lying in the XY and yz planes as shown in figure. 

we know, electric field at centre of circular coil is given by 

B = μ₀i/2πr 

∴Bp = μ₀×1/2πr = μ₀/2πr

BQ = μ₀√3/2πr = √3μ₀/2πr

now, here for coil P , magnetic field directed in upward and for coil Q , magnetic field directed in horizontally right as shown in figure. 

So, net magnetic field , Bnet = \bold{\sqrt{B_p^2+B_Q^2}}Bp2+BQ2 

Bnet = μ₀/2πr\bold{\sqrt{1^2+\sqrt{3}^2}}12+32 

= μ₀/2πr × 2 = μ₀/πr

Hence, answer is μ₀/or

Also direction of magnetic field, 

tanθ = Bp/BQ = 1/√3 = tan30° so, θ = 30° 

Hence, net magnetic field is directed above