Question

Two identical circular coils, p and q each of radius r, carrying current 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

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 = $\bold{\sqrt{B_p^2+B_Q^2}}$
Bnet = μ₀/2πr$\bold{\sqrt{1^2+\sqrt{3}^2}}$
= 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 directed in 30° with horizontal {BQ} .

Answer 2

Answer:

Hope this help you

Explanation:

Refer the given attachment