# Electron accelerated by potential difference

1. Dec 6, 2004

### gillgill

An electron is accelerated by a potential difference of, say, 100V. How much greater would its final speed be if it were accelerated with four times as much voltage?

2. Dec 6, 2004

### marlon

The corresponding energy is eV where e is the elementary charge and v is the applied potential. Note that this energy is kinetic in nature and therefore equal to 1/2mv²

regards
marlon

3. Dec 6, 2004

### gillgill

Ep=Ek
eV=1/2mv²
so...four times as much voltage= 16 times greater speed???

4. Dec 7, 2004

### marlon

So if the potential is 4 times bigger then the kinetic energy will get four times bigger. If A = mv²/2 or v = sqrt(2A/m) ; well then after the increase : 4A = mv²/2 or mv² =8A or v = sqrt(8a/m). Now if you devide sqrt(8A/m) by sqrt(2A/m) you acquire : sqrt(4) = 2. So the speed would be doubled...you see

regards
marlon

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