A parallel plate device is set up creating a uniform electric field between the

Question

A parallel plate device is set up creating a uniform electric field between the plates of magnitude E = 1 times 107 N/C as shown. A beam of charged particles (could be positively or negatively charged) is fired with speed v into the electric field region. You realize these particles will be deflected from traveling in a straight path by the electric field. But, you then realize that you could add a magnetic field to this region to allow the particles to travel through the parallel plate device in a straight path. Add magnetic field lines to the diagram that will allow the particles to travel through the region in a straight path. Explain how this is possible. Mathematically determine an expression for the magnitude of this magnetic field in terms of E, v, and any other relevant quantities that you need to introduce.

Explanation / Answer

a. I'm going to be a bit lazy and not draw this, but the field lines should point into the page (use x's), so a positive charge moving to the right would be pushed upward by the magnetic field (right hand rule), counteracting the force from the electric field.
b. For the particles to travel in a straight path, the Electric field and magnetic field need to exert the same force (in opposite directions, of course). The force from the electric field is F = qE, and the force from the magnetic field; F = qvB, so qE = qvB. The nonzero charge terms (q) cancel out, so E = vB, and therefore B = E/v

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