Answer to Question #93549 in Field Theory for Paul Ssemakula

Question

Two large parallel metal plates are separated by a distance d=1cm with the upper plate being 200V positive with respect to the lower plate. An electron with initial velocity 10^6 m/s is released upwards at the center of the lower plate. Calculate the time of flight of the electron? What will be the velocity of the electron upon striking the upper plate? How much energy is conveyed to the upper plate?

Answer 1

$$E=\frac{V}{d}=\frac{200}{0.01}=20000\frac{V}{m}$$

$$F=eE=(1.6\cdot 10^{-19})(20000)=3.2\cdot 10^{-15}N$$

From the conservation of energy:

$$a=\frac{F}{m}=\frac{3.2\cdot 10^{-15}}{9.1\cdot 10^{-31}}=3.5\cdot 10^{15}\frac{m}{s^2}$$

$$V^2=v^2+2ad=(10^6)^2+2(3.5\cdot 10^{15})(0.01)$$

The velocity of the electron upon striking the upper plate:

$$V=8.4\cdot 10^{6}\frac{m}{s}$$

The energy is conveyed to the upper plate is

$$E=eV=(1.6\cdot 10^{-19})(200)=3.2\cdot 10^{-17}J$$

The time of flight of the electron:

$$t=\frac{V-v}{a}=\frac{8.4\cdot 10^{6}-10^{6}}{3.5\cdot 10^{15}}=2.1\cdot 10^{-9}s=2.1\ ns$$