Current I is flowing in a conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

Step-by-step solution

The given current carrying conductor is shown below Magnetic field at the centre due to circular wire, B₁= ₀ I 2 r 270 360 = ₀ I 2 r 3 4 B₁= 3 ₀ I 8 r [in downward to the plane of paper] Magnetic field at centre O due current carrying wire A B will be zero because point O lies along A B B₂=0 Magnetic field at O due to current carrying wire C DB₃= ₀ I 4 r (in downward to the plane of paper) Net magnetic field at the centre, aligned B_ net &=B₁+B₂+B₃= 3 ₀ I 8 r +0+ ₀ I 4 r &= ₀ I r [ 3 8 + 1 4 ]= ₀ I 4 r [ 3 2 +1 ] a