Retarded position of moving point charge

Retarded position of moving point charge (3D animation) Right click on number s and check Animation on At time

a spherical light wave is emitted from field point

[position vector

] to the past, and the point charge

is moving backwards in time from its present position

[position vector

] ("video backwards"). The point

where this wave "arrests" the charge is the retarded point. The retarded time and position are

Note that both these retarded quantities are implicit functions of

and

for given function

for the motion of

. Now, with "video forward" : when the charge

is on the retarded point

at the retarded time

, the electromagnetic disturbance (field) caused by it is travelling with speed

and arrives on field point

[position vector

] at the present time

the charge being on the present position

. For charge

living deep in the past (not created close to the present time) the retarded position exists and it's unique for given

and function

. The proof is based on the assumption that the speed of the charge

is at any time less than the speed of light

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