Here is a thought experiment on Special Relativity involving charges which are rest with respect to each other.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a configuration of charges as shown in the image. Four identical charges (q) are placed at the corners of a square with an opposite charge at the centre (Q). The value of Q is such that the whole configuration is stable and no charge experiences a net force.

It can be shown that for this to work

[Q]/[q]= 1+[itex]\sqrt{2^{3}}[/itex]

Now consider the same configuration of charges in an inertial frame of reference moving at a velocity v relative to a stationary observer. This observer should find the square to be squeezed into a rectangle as the length in the direction of motion will contract.

It should be assumed that the charges would still not experience a net force - as an observer in the same frame of reference as the charge system will not find the charges to be moving.

If the stationary observer calculates the equilibrium of the charges, he should find a new ratio for the charges:

[Q]/[q]= 1+ [itex]\sqrt{(1+\gamma^{2})^{3}}[/itex]

where

[itex]\gamma[/itex] = [itex]\sqrt{ 1- \frac{v^{2}}{c^{2}}}[/itex]

Thus, the observer moving along with the charges will find one ratio for the charges while the observer at rest will observe another ratio.

But how can this be since they are the same system of charges and charge is itself an invariant under relativity?

I hope I have been clear enough. Please ask me if you'd like something cleared.

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# A thought experiment on relativistic Electrostatics

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