Problem 1:

1. Which way is the electron deflected?
2. Add a magnetic field to the region between the plates. What direction should it be to cancel the deflection of the electron by the electric field?
3. The electric field magnitude is 1000 V/m, and the electron moves at 2.5 x 10⁵ m/s. What must be the magnitude of the magnetic field for no electron deflection?

1. This is just an electric field problem. Define a coordinate system with x to the right (direction of the electron), y upwards (opposite to the field) and z out of the page. Then using

      F = qE

   with E = -Ej (downwards) and q = -|e| (electrons have negative charge), so

      F = (-|e|)(-Ej) = +|e|E j

   i.e. the force is upwards.

2. We want the magnetic force to be downwards (-j). The magnetic force is given by

      F = qv x B

   where q = -|e|. Ignore the magnitudes of the vectors, and just consider directions (and signs) and we have

      -j = (-)(i x ?)

   recall    i x k = -j

   so what we need i x -k = j which along with the sign of the electron's charge gives us the correct direction. Thus the B field must be in the -k direction, i.e. into the page.

3. Now, we want the forces to balance, i.e.   qE = qvB

   or     B = E/v

   or   B = (1000 V/m)/(2.5 x 10⁵m/s) = 4 x 10^-3 T

   This is just the `velocity selector' Tipler discusses on pg 791...

Problem 2
Test 3
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