[LECS/EM-07001] Current and Current Conservation

In this section we compute the leading term in the magnetic field of a current loop at large distances and obtain an expression for the magnetic moment of the loop.

The equation of continuity for conservation of electric is derived. An expression for current in a wire is obtained in terms of number of electrons per unit volume.

in this section the rule  about  the direction of cross product the cross product of two vectors  is explained.

The vector potential is introduced using the Maxwell's equation ∇×B→=0" role="presentation">∇×B⃗ =0

is derived. The expression for the magnetic field is obtained as volume integral, the Biot Savart law, is derived. The expressions for the magnetic field for the surface current and the line current are given.

 In this section we compute the leading term in the magnetic field of a current loop at large distances and obtain an expression for the magnetic moment of the loop.

For a volume distribution of current an expression for magnetization density,{\it i.e.} the magnetic moment per unit volume, is obtained. An expression for the magnetic field at large distances, in terms of magnetization density,  is derived.

Direction convention for Ampere's law is explained

The Biot Savart law for current carrying wire is explained.

The equation of continuity appears in different branches of physics. It represents a local conservation law. In order to be consistent with requirement if special relativity every conserved quantity must come with a current which gives the flow of the conserved quantity across a surface and the two must obey equation of continuity. In this section we discuss these aspects of conservation laws.

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Expressions for  force on line  and volume elements of a current in magnetic field are derived. 

The magnetic moment for a point particle is shown to be related  to the angular momentum ℓ" role="presentation">ℓ

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The meaning of charge conservation is discussed. It is known to be mathematically represented by  the equation of continuity. It is argued that special relativity requires that there should be  a 'current' associated with  every conserved quantity.