Problem 6 is a bit sneaky. Think about how the capacitance relates to the geometry of the capacitor (C ~ A/d), and how those distances are contracted. If you move toward the plates along the axis, the plate spacing is contracted, but area remains the same. If you move perpendicular to the axis, the spacing is the same, but what happens to the surface charge density?
As one hint, charge is invariant, and always the same no matter what relative motion there is.
As a stronger hint, I was about to post my notes on radiation, which starts out with the fields of moving charges ...
For 7, note that F = qE = dp/dt, with momentum p=(gamma)mv. Then
dp/dt = (gamma) m dv/dt + mv d(gamma)/dt
With the definition of gamma, grind through the derivatives and it should work out.
I'm going to run through #6 and 7 tomorrow in class in any event, just to make sure you know how to get started.
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