Answer to Question #265918 in Physics for Crystal

Question

An electron moving 5.0×10^6m/s is shot parallel to an electric field of strengHth 1×10^3N/c Arranged so as to retard its motion

a. How far will the electron travel in the field before coming momentarily to rest.

b. If the field ends suddenly after 0.75cm, what fraction of its initial energy will the electron lose in passing through it.

2. A vaccum diode contsists of a cylindrical cathode of radius 0.05cm mounted coaxially inside a cylindrical anode of radius 0.45cm. If the anode-cathode voltage is 400V and the electron leaves the anode with zero speed, calculate its speed when it strikes the anode. What is the flux density of the magnetic field that must be applied along the axis in order to just prevent the electrons from striking the anode?

Answer 1

a. The acceleration:

$$a=F/m=Eq/m.$$

The distance:

$$d=\frac{v^2}{2a}=\frac{mv^2}{2Eq}=0.07\text{ m}.$$

b. Energy conservation:

$$KE_2=W+KE_1,\\\space\\ \Delta KE=KE_2-KE_1=W,\\\space\\ W=-Vq=qEL,\\\space\\ \Delta KE=qEL.\\\space\\ \frac{\Delta KE}{KE_1}=\frac{qEL}{KE_1}=\frac{2qEL}{mv^2}=0.1$$