A long straight wire carrying current I is bent into the shape as shown in the figure. The circular portion of the wire has radius `(10//pi)m`. The centre of this circle is at a distance `1m` from the straight portion of the wire. What is the magnitude of the magnetic field at the centre of the circular portion? Given `pi^2=10`.

Answer

Zero

Explanation

Magnetic field at the centre O of cicular coil due to current is, `B_1=(mu_0)/(4pi)(2piI)/((10//pi))=(mu_0)/(4pi)(pi^2I)/(5)`. It is directed into the plane of paper. Magnetic field at O due to current through straight wire portion 1, `B_2=(mu_0)/(4pi)*(2I)/(1)=(mu_0)/(4pi)2I`, It is directed outwards from the plane of paper.
Magnetic field at O due to current through straight portion 3 is, `B_3=0`
(`:'` O lies on the axis of the wire portion 3).
Net magnetic field at O is, `B=B_1-B_2+B_3` directed inwards to the plane of paper.
`B=(mu_0I)/(4pi)[(pi^2)/(5)-2]=(mu_0I)/(4pi)[10/5-2]=0`