An easy way to accelerate a charge is to allow it to move through a potential difference. Consider a parallel-plate capacitor with a uniform field E, and a potential difference with a magnitude of:
|DV| = Ed, where d is the plate separation.
A charge released from rest in the capacitor will accelerate towards one of the plates. Cutting a hole in the plate allows it to escape.
Apply conservation of energy ideas to find the speed of the charge when it leaves the capacitor:
Ui + Ki + Wnc = Uf + Kf
There are no non-conservative forces acting, the initial kinetic energy is zero, and we can define the plate where the charge exits the capacitor as the zero of potential energy (i.e., Uf = 0).
This gives Kf = 1/2 mv2 = q DV so:
v | = | ( |
|
)1/2 |
Can you think of any practical applications of such a system for accelerating charges?
There is a useful energy unit that's particularly applicable to accelerating electrons, protons, or ions. This unit is the electron-volt (eV).
1 eV is the amount of energy associated with moving one electron through a potential difference of 1 volt.
1 eV = 1.6 x 10-19 J