Three rings, each with equal radius ' r ' are placed mutually perpendicular to each other and each having centre at the origin of coordinate system. ' I ' is current passing through each ring. The magnetic field value at the common centre is

Step-by-step solution

The magnetic field at the centre of the ring is aligned & B = ₀ 4 i r (2 )= ₀ I 2 R & B₁ = ₀ I 2 r i , B₂ = ₀ I 2 r j , B₃ = ₀ I 2 R k & ~B ₀ = B ₁ + B ₂ + B ₃ = ₀ I 2 r ( i + j + k ) & B₀= ₀ I 24 1^2+1^2+1^2 = 3 ₀ I 2 r aligned