Electrons are passed through a region containing both a uniform electric field a

Question

Electrons are passed through a region containing both a uniform electric field and a uniform magnetic field.

- The electrons propagate in the positive x-direction

- The electric field points in the negative z-direction

- The magnetic field points in the positive y-direction

a) If the electric field and magnetic fields are adjusted such athat the electrons are not deflected, express the velocity in terms of the electric field E and the magnetic field B. Show all of the steps that lead to the answer.

b) If the electric field is turned off, magnetic field will cause the electrons to move along a circular path with a radius of curvature R. With the electric field turned off, what is the charge to mass ratio q/m in terms of the electric field E, the magnetic field B and the radius of curvature R?

Explanation / Answer

a) so q vB = q E

so v = E/B

b) q v B = mv^2/r

so q B = m v/r

q/m = v/(B R)

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