Magnetic field

We will now look at the properties of the magnetic field which are related to the flux and circullation of the vector field to express the basic laws of magnetic field. We already know how to represent electric field graphically and unlike any other vector field magnetic field B can be represented with the help of field lines drawn in such a way that tangent to those lines at any point concides with the direction of the magnetic field B and the density of the lines is proportional to the magnitude of the vector at a given point. we would now consider the basic laws of magnetic field....
(1) Gauss's Theorem for the field B:-
It says that "Flux of B through any closed surface is equal to zero". i.e.,

This says that field lines of vector B neither begning nor end and therefore field lines of vector B emerging from any volume closed by surface S is always equal to the number of lines entering this volume. This law also indicate the absence of magnetic charges on which field lines of vector B begin or terminate i.e., magnetic fields has no sources as charges are for electric field.

(2) Theorem of circulation of magnetic field:-
It states that " Circulation of vector B around a arbitrary contour C is equal to the product of magnetic permeability times the algebric sum of currents enveloped by the contour C".

The current is assumed to be positive if its direction is connected with the direction of the circumvention of the contour C through the right hand screw rule and is negative if it is in opposite direction. This theorem can be proved by means of Biot Savart's Law. This theorem plays same role for magnetic field as Gauss's theorem plays for electric field.

For full length notes on magnetic effect of current and magnetism visit

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