An electron entering Thomson\'s e / m apparatus (Figure 3.2 and 3.3) has an init

Question

An electron entering Thomson's e/m apparatus (Figure 3.2 and 3.3) has an initial velocity (in horizontal direction only) of 0.6 107 m/s. Lying around the lab is a permanent horseshoe magnet of strength 1.0 10-2 T, which you would like to use.

(a) What electric field will you need in order to produce zero deflection of the electrons as they travel through the apparatus? (b) When the magnetic field is turned off, but the same electric field remains, how large a deflection will occur if the region of nonzero E and B fields is 2 cm long?

Explanation / Answer

a)

here

E = v *B

E = 0.6 * 10^7 * 1 * 10^-2

E = 6 * 10^4 V /m

b)

You have acceleration ( = F/m = qE/m) and horizontal distance,
and initial vertical velocity is zero.
You can look up the mass and charge of an electron.
From the horizontal distance, you have time = 0.02 m divided by 4 x 10^6 m/s
= 5.0 x 10^(-9) seconds. Then use
y = v0 t + (1/2) a t^2
= (0) + (1/2) (qE/m) t^2
to obtain y, the vertical distance.

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