An electron enters a region between two capacitor plates with equal and opposite

Question

An electron enters a region between two capacitor plates with equal and opposite charges. The plates are L=0.2 m by d=0.08 m, and the gap between the plates is h=0.002 m. During a short time interval of =0.002 s, while between the plates and far from the edges, the change of momentum is =<0,-9x10-17,0> kg m/s. Ignore gravitational effects here since they are so weak compared to electric effects. (a) What is the electric field vector between the plates (far from the edges)? (hint: momentum principle) (b) What is the charge (magnitude and sign) on the upper plate?

Explanation / Answer

Rate of change of momentum = Force (as per newton definition )

Force = 9x10^-17 / 0.002 = -4.5 * 10^-14 N
therefor , Electric field = Force / q (charge on electron ) = -4.5 * 10^-14 / 1.60 × 10^-19

= -281250 volts (answer-1)

Electric field,E= -281250 = Q/eA (e=permissivity=8.854 x 10^-12,A=L*d=0.2 * 0.08 m = 0.016m)
solving for Q (charge), we get = 3.98 * 10^-8 Coulombs (answer)

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