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Extra Credit:

Suppose there were two electrons, travelling side by side, a distance d apart. They are both travelling at velocity v to the right.

a$)$ Find the electric and magnetic forces on the top charge in terms of the givens.

b$)$ As seen in class, if $\backslash ($ v $\backslash )$ gets larger, this will make $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$B$\}\}\backslash )$ larger, but not $\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$E$\}\}\backslash ).$ So it may be reasonable to think that for some $\backslash ($ v $\backslash ),$ the magnetic force will dominate the electric force. Since this would result in the two electrons attracting each other, we run afoul of the principle of relativity, which predicts the result that since the electrons are repelled in one reference frame they must be repelled in all reference frames. Determine the speed at which the electric force repelling the electrons is just balanced by the magnetic force attracting them, and explain how this result solves our problem.