a. How much energy in joules is required to move a charge of 12 μC through a difference in potential of 6 V?
b. For part (a), find the energy in electron-volts.
(a)
Calculate the energy, \(W\) required to move the charge through the difference in potential. \(W=Q V\)
Substitute \(12 \mu \mathrm{C}\) for \(Q\) and \(6 \mathrm{~V}\) for \(V\)
$$ \begin{aligned} W &=(12 \mu \mathrm{C})(6 \mathrm{~V}) \\ &=72 \mu \mathrm{J} \end{aligned} $$
Thus, the energy, \(W\) required to move the charge through the difference in potential is \(72 \mu \mathrm{J}\).
(b)
Consider the relation between electron volt and Joule.
$$ \begin{aligned} &1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J} \\ &1 \mathrm{~J}=\frac{1}{1.6 \times 10^{-19}} \mathrm{eV} \\ &=6.25 \times 10^{18} \mathrm{eV} \end{aligned} $$
Convert the energy in electron volts \(\mathrm{eV}\).
$$ \begin{aligned} W &=72 \times 10^{-6} \mathrm{~J} \\ &=\left(72 \times 10^{-6}\right)\left(6.25 \times 10^{18} \mathrm{eV}\right) \\ &=45 \times 10^{13} \mathrm{eV} \end{aligned} $$
Thus, the energy in electron volts \(\mathrm{eV}\) is \(45 \times 10^{13} \mathrm{eV}\).