A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R . The total magnetic field at the centre P at the loop is

Step-by-step solution

The magnetic field at the centre of an arc subtended at an angle is given by B = ₀ i 2 R 2 Then, the magnetic field due to larger arc A B is B ₁= ₀ i ₁ 2 R 270 2 which acts in inward direction according to right hand thumb rule. And magnetic field due to smaller arc A B is B ₂= ₀ i ₂ 2 R 90 2 which acts in outward direction. The resultant magnetic field aligned & B _ R = B ₁+ B ₂ & =- ₀ i ₁ 270 4 R + ₀ i ₂ 90 4 R [From Eq. (i) and (ii)] aligned which acts in inward direction as B ₁> B ₂ . Two arcs can also be seen