(a) Biot Savart Law
It states that the magnetic field strength (dB) produced due to a current element (of current I and length dl) at a point having position
vector r relative to current element is
where μ0 is permeability of free space. Its value is
The magnitude of magnetic field is
where q is the angle between current element I vector dl and position vector r.
The direction of magnetic field vector dB is perpendicular to the plane containing I vector dl and vector r.
Magnetic Field at the centre of circular loop: Consider a circular coil of radius R carrying current I in anticlockwise direction. Say, O is the centre of coil, at which magnetic field is to be computed. The coil may be supposed to be formed of a large number of current elements. Consider a small current element ‘ab’ of length Δl. According to Biot Savart law the magnetic field due to current element ‘ab’ at centre O is
where q is angle between current element ab and the line joining the element to the centre O. Here q = 90°, because current element at each point of circular path is perpendicular to the radius. Therefore magnetic field produced at O, due to current element ab is
According to Maxwell’s right hand rule, the direction of magnetic field at O is upward, perpendicular to the plane of coil. The direction of magnetic field due to all current elements is the same. Therefore the resultant magnetic field at the centre will be the sum of magnetic fields due to all current elements. Thus
Here current in the coil is anticlockwise and the direction of magnetic field is perpendicular to the plane of coil upward; but if the current in the coil is clockwise, then the direction of magnetic field will be perpendicular to the plane of coil downward.
