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in Physics by (53.2k points)

Derive the expression for the magnetic field on the axis if a circular current loop, using biot-savart’s law.

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Consider a circular loop in the Y - Z Plane with its centre at the origin O. 

Let R be the radius of the loop and I is the steady current through the loop in anti-clock wise direction. 

Consider a point P on the axis of the loop coinciding with X-axis at a distance x from O.

The magnitude of magnetic field at P due to current element dl is given by,

The element \(d\vec l\) is in Y - Z plane. Unit vector is in the x - y plane, Hence sin90°= 1

The direction of dB is perpendicular to the plane formed by \(d\vec l\) and \(\vec r\) Resolving dB into two components.

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