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Lets suppose a charge Q placed on a small sphere centered at the origin of our c

ID: 2139761 • Letter: L

Question

Lets suppose a charge Q placed on a small sphere centered at the origin of our coordinate system. A time t = 0, the sphere explodes, the explosion generates a current which, by the problem's symetry, has to be radial : .

Knowing this, the expression for the vector potential A has to be radial and thus the current distribution does not generate any magnetic field since = 0

Use the Ampère-Maxwell law to show this explicitly.

The problem was solved in another topic, but without using Ampère-Maxwell law.


Explanation / Answer

charge on small sphere is Q

the current generated after explosion is

I = (Q/t)

where t is time

the power dissipated by the sphere is

P = V x I

where V is the applied potential difference

the electrical energy is

E = V x I x t