2) An electron enters a region between two capacitor plates with equal and oppos

Question

2) An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.1 m by d=0.05 m, and the gap between the plates is h=0.002 m. During a short time interval of delta t =0.002 s, while between the plates and far from the edges, the change of momentum is delta P vector = kg m/s. Ignore gravitational effects since they are so weak compared to electric effects. (a) What is the electric field vector between the plates (it is not shown on the figure)? (hint: momentum principle) (b) What is the charge (magnitude and sign) on the upper plate? (c) What is the potential difference delta V = Vtop - Vbottom?

Explanation / Answer

a)Change in velocity=a*t=qEt/m

Change in momentum=m*change in velocity=qEt=-1.6*10^-19*E*0.002=-9*10^-17

E=281250N/C

E=(0,281250,0)

b)E=q/epsilon_0

q=E*epsilon_0=281250*8.854*10^-12=-2.49*10^-6C

c)Delta V=E.h=281250*0.002=562.5V

The upper plate is negatively charged since the electron moves downward during the plate motion.

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