In electrodynamics we have E = E(r, t) and B = B(r, t) satisfying Maxwell's equations....

 

Transcribed Image Text:

In electrodynamics we have E = E(r, t) and B = B(r, t) satisfying Maxwell's equations. In this case we can introduce electromagnetic potentials A= A(r, t) and V = V(r, t), where the magnetic field is defined in terms of the vector potential as B = V x A(r, t). a) Show that this formulation corresponds to an electric field which is defined in terms of A and V as, E-VV- OÃ Ət b) Given these definitions of electric and magnetic fields in terms of the potentias, determine the expres- sions for the electromagnetic sources p(r, t) and J(F, t). In electrodynamics we have E = E(r, t) and B = B(r, t) satisfying Maxwell's equations. In this case we can introduce electromagnetic potentials A= A(r, t) and V = V(r, t), where the magnetic field is defined in terms of the vector potential as B = V x A(r, t). a) Show that this formulation corresponds to an electric field which is defined in terms of A and V as, E-VV- OÃ Ət b) Given these definitions of electric and magnetic fields in terms of the potentias, determine the expres- sions for the electromagnetic sources p(r, t) and J(F, t).

Answer rating: 100% (QA)

SOLUTION a We start with the Maxwells equations in the vector form E 0 1 E Bt 2 B 0 3 B 0J 4 where E is the electric field B is the magnetic field is the charge density J is the current density 0 is t... View the full answer