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# Potential & Field Formulation for Time Varying Fields Notes | EduRev

## IIT JAM : Potential & Field Formulation for Time Varying Fields Notes | EduRev

The document Potential & Field Formulation for Time Varying Fields Notes | EduRev is a part of the IIT JAM Course Electricity & Magnetism.
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Scalar and Vector Potentials

We want general solution to Maxwell's Equations,  Given what are the fields From equation (ii) we can still write   Now from equation (i) From equation (iv) Equations (1) and (2) contain all the information of Maxwell’s equations. Thus we need to calculate only four components (one for V and three for instead of six components (three for and three for Example 1:  In an infinite straight wire constant current I0 is turned on abruptly at t = 0 . Then corresponding retarded potentials are given by . Find the fields corresponding to these potentials.

The electric field is And the magnetic field is Gauge Transformation

Suppose we have two sets of potentials, which correspond to the same electric and magnetic fields.

Thus, Since Two potentials also give the same So,  Actually, we might as well absorb k (t ) into λ, defining a new λ by adding to the old one. This will not affect the gradient of λ ; it just adds It follows that Conclusion: For any old scalar function λ , we can add provided we simultaneously subtract from V. None of these will affect the physical quantities and Such changes in V and are called gauge transformations.

Coulomb and Lorentz Gauge Lorentz Gauge condition is Since and Using Lorentz Gauge condition The virtue of the Lorentz gauge is that it treats V and on an equal footing: the same

differential operator (called the d' Alembertian) occurs in both equations:  Example 2: For a vector potential the divergence of is where Q0 is a constant of appropriate dimensions. Find the corresponding scalar potential that makes and V Lorentz gauge invariant. Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

## Electricity & Magnetism

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