C URRENT L OOP In this section, we shall evaluate the magnetic field due to a circular coil along its axis. The evaluation entails summing up the effect of infinitesimal current elements ( I d l ) mentioned in the previous section. We assume that the current I is steady and that the evaluation is carried out in free space (i.e., vacuum). Figure .
depicts a circular loop carrying a steady current I . The loop is placed in the y-z plane with its centre at the origin O and has a radius R . The x -axis is the axis of the loop. We wish to calculate the magnetic field at the point P on this axis.
Let x be the distance of P from the centre O of the loop. Consider a conducting element d l of the loop. This is shown in Fig. .
. The magnitude d B of the magnetic field due to d l is given by the Biot-Savart law [Eq. . (a)], I d dB µ l × r ( .
) Now r = x + R . Further, any element of the loop will be perpendicular to the displacement vector from the element to the axial point. For example, the element d l in Fig. .
is in the y-z plane whereas the displacement vector r from d l to the axial point P is in the x-y plane. Hence | d l × r |= r dl . Thus,