Introduction to Mathematical Physics/Electromagnetism/Exercises

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Exercice:

exoeqhelmoltz

Assume constitutive relations to be:

where represents temporal convolution\index{convolution} (value of field at time S depends on values of at preceeding times) and

Show that in harmonical regime () and without any charges field verifies Helmholtz equation :

Give the expression of .

Exercice:

Show (see ([#References

Exercice:

Proove charge conservation equation eqconsdelacharge from Maxwell equations.

Exercice:

Give the expression of electrical potential created by quadripole .

Exercice:

Show from the expression of magnetic energy that force acting on a point charge with velocity is: