A charge q moves with speed v parallel to a long rod with linear (At rest) charg

Question

A charge q moves with speed v parallel to a long rod with linear (At rest) charge density lambda., as shown in Fig. 5.30. The rod is at rest. If the charge q is a distance r from the rod, the force on it is simply F = qE = q lambda/2pirepsilon0. Now consider the setup in the frame that moves along with the charge q. What is the force on the charge q in this new frame? Solve this by: transforming the force from the old frame to the new frame, without caring about what causes the force in the new frame; calculating the electric force in the new frame.

Explanation / Answer

when both are in motion, the relative velocity V' comes into play

which is equals to V1-V2 as both are moivng in same direction.

then force =qV'B

electrical force F= Eq

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