In many applications, oppositely charged parallel plates $($with small holes cut for the beam to pass through$)$ are used to accelerate beams of charged particles. In this example, an electron is injected at $2\mathrm{.}0{10}^7\frac{m}{s}$ into the space between the plates. The plates are $5$ cm apart.

Mathematical Analysis ${?}^{23}$

a$.$ If the electron exits the device at $2\mathrm{.}5{10}^7\frac{m}{s},$ what is the potential difference between the plates?

b$.$ If a proton entered the same device at the same speed, with what speed would it exit the device?

c$.$ What is the electric field between the plates?

Electric Potential $-57$