Question

6. Recall from physics 9A the trajectory of a point on the edge of a wheel that rolls without slipping in the +x direction. For a particle of charge q and mass m moving in the xy plane, subject to a uniform magnetic field B pointing in the +z direction, what uniform electric field will produce this trajectory?

Answer 1

For a particle with charge +q and moving with a velocity v, the force on it due to an external magnetic field is given by:

this particle can have a motion similar to a point on the edge of a wheel when it is rolling without slipping in the positive x direction if the magnetic field is applied in the z direction and the electric field is applied in the positive x direction. The electric field component imparts a forward moving velocity along x direction while the magnetic field component imparts the circular motion along the direction of motion.