Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.
Draw the magnetic field lines due to a circular wire carrying current I.
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Imagine a circular coil of radius R with centre O.Let the current flowing through the circular loop be I. suppose P is any point on the axis at a distance of r from the centre 0. Let the circular coil be made up of a large number of small elements of current, each having a length of dl. According to Biot-Savart's law, the magnetic field at Point P will be
|dl×r|=rdl [ ∵ Both are perpendicular]
Here, r is the position vector of point O from the current element.
dB has two components i.e.,dBxanddBy.
dBy is cancelled out and only the x-component remains.