We will use the formulas developed in the previous section to find the potentials and the fields. The reason is very subtle: for the integral to be equal to the total charge, the charge distribution has to be taken at a specific time. However, we are obliged to evaluate the distribution at different times for each point! Thus, the charged particle is "smeared" out! Even though we are considering a point particle, the formula is still wrong, since the correction factor doesn't depend on geometric size! Suppose the particle is a box of length a and is moving towards us.

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We will use the formulas developed in the previous section to find the potentials and the fields. The reason is very subtle: for the integral to be equal to the total charge, the charge distribution has to be taken at a specific time. However, we are obliged to evaluate the distribution at different times for each point! Thus, the charged particle is "smeared" out! Even though we are considering a point particle, the formula is still wrong, since the correction factor doesn't depend on geometric size!

Suppose the particle is a box of length a and is moving towards us. However, we will observe the particle to have length b, because the light that is simultaneously reaching our eyes from the front and back of the box originated from different times.

These are the Lienard-Wiechert Potentials for a moving charge. The correction factors are for the components of velocity pointing to the point we are measuring the potentials at. From Wikibooks, open books for an open world. This is not an effect of length contraction; this is rather more similar to the Doppler shift. Category : Book:Electrodynamics. Namespaces Book Discussion. Views Read Edit View history.

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## Liénard–Wiechert potential

Built directly from Maxwell's equations , these describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion, but are not corrected for quantum-mechanical effects. Electromagnetic radiation in the form of waves can be obtained from these potentials. We can calculate the electric and magnetic fields directly from the potentials using the definitions:. The calculation is nontrivial and requires a number of steps.

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## The Liénard–Wiechert potentials and the solution for Maxwell’s equations

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