# How to find electron speed

According to the standard planetary model of atom, any atom is similar to the Solar system. A role of the Sun is played by a massive kernel in the center (where the protons bearing positive charges are concentrated), around which negatively charged electrons rotate. In general atom is neutral as the quantity of protons and electrons is identical, and the neutrons which are in a kernel together with protons do not bear in general any charge.

## Instruction

1. For example, you should solve such problem. The electron moves in uniform magnetic field with induction size In, describing at the same time ideally circular trajectory. It is affected by Fl Lorentz force. Centripetal acceleration of an electron is equal "and". It is required to calculate the speed of the movement of an electron.

2. For a start remember what is Lorentz force and as it is calculated. It is force with which the electromagnetic field affects single charged particle. In your case, under the terms of a task (the electron is in magnetic field, moves on a circle of constant radius), Lorentz force will be centripetal force and to be calculated on the following formula: Fl = evB. The sizes Fl and B are given you under the terms of a task, electron charge size e easily is in any reference book.

3. On the other hand, Lorentz force (as well as any other force) can be expressed on the following formula: Fl = ma. The size of mass of an electron of m also without effort is by means of reference books.

4. Equalizing these expressions, you will see that evB is equal to ma. The only size unknown to you – that speed of v which also should be found. By elementary transformation, you receive: V = ma/eB. Having substituted in a formula sizes known to you (both the data under the terms of a task and found independently), receive the answer.

5. Well, and how to be, for example, if neither the size of induction is unknown to you In, nor Fl Lorentz force, and instead of them only a radius of a circle of r on which that electron rotates is given? How in that case to determine its speed? Remember a formula of centripetal acceleration: and = v2/r. From here: v2 = ar. After extraction of a square root from works of sizes of centripetal acceleration and radius of a circle, you also receive the required speed of an electron.

Author: «MirrorInfo» Dream Team