A current circular conducting loop exerts a magnetic field both inside and outside it. The magnetic field at the cetre of a current loop of radius 'R' and carrying a current I is given as :
`B = (mu_0 I)/(2 R)`

The magnetic field lines due to a circular current loop form closed loops. The direction of the magnetic field is given by the right hand thumb rule, which states that if one curls the palm of his right hand around the current loop with the fingers pointing in the direction of the current, the right hand thumb will give the direction of the magnetic field. From this law it is clear that the direction of magnetic field `vecB` is always perpendicular to the direction of flow of current or perpendicular to the plane of circular current loop.
Determine the magnetic field at the centre point O due to two concentric semicircular loops of radii `R_1 and R_2` carrying a current I, when the loops of radii `R_1 and R_2` carrying a current I, when the loops are arranged as shown in Fig.

Explanation

For a semicircular loop, field `B = (mu_0 I)/(4R)`
In the arrangment shown in Fig., field `B_1` due to semicicular loop QR and field `B_2` due to semicircular loop SP are
`vecB_1 = (mu_0 I)/(4 R_1) ox and vecB_2 = (mu_0 I)/(4 R_2) o.`
`:. vecB = vecB_1 + vecB_2 = (mu_0 I)/(4) [1/(R_1) - 1/(R_2)] ox`