Figure shows a current loop having two circular arcs joined by two radial lines. Find the magnetic field B at the centre O.

Explanation

Solution: As the point O is on the line AD, the magnetic
field at O due to AD is zero. Similarly , the field at O
due to BC is also zero. The field at the centre of a
`circular current loop is given by B= ((mu_0)i/2a). The field due
to the circular arc BA will be
` B_1=(theta/ 2pi)((mu_0)i/2a)`
The right-hand thumb rule shows that the field is
coming out of the plane of the figure. The field due to
the circular arc DC is
` B_2= (theta/2 pi)((mu_0)i/2b) `
` going into the plane of the figure. The resultant field at
O is
B= ((B_1)-(B_2))= ((mu_0)i theta(b-a)/4 pi ab)`
coming out of the plane.