5. The two 4 am-long para el electrodes .n the figure are spaced 1.0 m apart. An

Question

5. The two 4 am-long para el electrodes .n the figure are spaced 1.0 m apart. An electron enters the plates from one end, an equal distance om both electroc es A potential differenceV-500 V across the electrodes deflects the particle so that it strikes the outer end of the upper electrode. What magnetic field strength and direction will allow the particle to pass through undeflected while the 300 V potential difference is applied? Assume that both the electric and magnetic fields are confined to the space between the electrodes. Do you need to take into account the force of gravity? Why or why not?

Explanation / Answer

E = V / d = 300 /1 = 300 N/C

acceleration, a = Fe / m = q E / m

a = (1.60 x 10^-19)(300) / (9.109x 10^-31)

a = 5.27 x 10^13 m/s^2

perpendicular to the electrodes,

d = v0 t + a t^2 / 2

0.5 = 0 + (5.27 x 10^13) t^2 / 2

t = 1.38 x 10^-7 sec

v = (0.04) / t = 2.90 x 10^5 m/s

now to go undeflected,

Fnet = Fm + Fe = 0

q V B - q E = 0

B = E / v = (300) / (2.90 x 10^5)

B = 1.03 x 10^-3 T or 1.03 mT

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