k = 8.99 x 10⁹ Nm²C⁻²

1. Convert 5 x 10⁻¹³ J to MeV.

${\displaystyle {\frac {5\times 10^{-13}}{1.6\times 10^{-19}}}=3125000{\mbox{ eV}}=3.125{\mbox{ MeV}}}$

2. Convert 0.9 GeV to J.

${\displaystyle 0.9\times 10^{9}\times 1.6\times 10^{-19}=1.44\times 10^{-10}{\mbox{ J}}}$

3. What is the potential energy of an electron at the negatively charged plate of a uniform electric field when the potential difference between the two plates is 100V?

${\displaystyle \epsilon _{elec}=V_{elec}q=100\times 1.6\times 10^{-19}=1.6\times 10^{-17}{\mbox{ J}}=0.1{\mbox{ keV}}}$

4. What is the potential energy of a 2C charge 2 cm from a 0.5C charge?

${\displaystyle \epsilon _{elec}={\frac {kQq}{r}}={\frac {8.99\times 10^{9}\times 2\times 0.5}{0.02}}=4.5\times 10^{11}{\mbox{ J}}}$

Remember, coulombs are big!

5. What is represented by the gradient of a graph of electric potential energy against distance from some charge?

Force exerted on the charge with that energy.