Coupon Accepted Successfully!


Magnetic Scalar Potential

The magnetic scalar potential is a useful tool in describing the magnetic field around a current source. It is defined only in regions of space in the absence of currents.
We know from Ampere’s law that Description: 57472.png for a steady current. If the current density Description: 57462.png is zero in some region of space then we have,
Description: 57455.png
and so we can write the magnetic field Description: 57448.png as the gradient of a scalar quantity as,
Description: 57441.png
where Vm is called the magnetic scalar potential. It is expressed in amperes.

Magnetic Vector Potential

We know that the divergence of magnetic flux density is always zero everywhere Description: 57286.png. Hence, Description: 57276.png can be expressed as the curl of some other vector function. We designate this vector as Description: 57267.png which is known as the magnetic vector potential.
Description: 57260.png

Magnetic vector potential is expressed in webers per metre (Wb/m) or in newtons per ampere (N/A) or in volt-second per metre (V-s/m); with its dimension as MLI-1T-2.
Now, by Ampere’s law,
Description: 76235.png
If we let, Description: 76226.png, which is called Coulomb’s gauge condition then, we obtain,
Description: 76219.png
This is similar to Poisson’s equation of electrostatics, Description: 76212.png, whose solution is Description: 76204.png. By comparison, we get the magnetic vector potential as,
Description: 76195.png

The concept of magnetic vector potential is extremely useful for studying radiation in transmission lines, waveguides, antennas, etc.

Derivation of Magnetic Flux in terms of Magnetic Vector Potential

We know that the magnetic flux coming out of a surface is given as,
Description: 75746.png
where Description: 75739.png is the magnetic flux density. Writing this in terms of magnetic vector potential as Description: 75731.png and applying Stokes’ theorem, we obtain,
Description: 75714.png

Test Your Skills Now!
Take a Quiz now
Reviewer Name