CURRENT LOOP

CURRENT LOOP 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 dl) 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 dl of the loop. This is shown in Fig. .

. The magnitude dB of the magnetic field due to dl is given by the Biot-Savart law [Eq. . (a)], I d dB µ l × r ( .

) Now r2 = x2 + R2 . Further, any element of the loop will be perpendicular to the displacement vector from the element to the axial point. For example, the element dl in Fig. .

is in the y-z plane whereas the displacement vector r from dl to the axial point P is in the x-y plane. Hence |dl × r|=r dl. Thus,