9.3 Conservation of Electric Energy

2.3 Conservation of Electrical Energy

We can solve a whole class of problems by using the fact that electrical energy + kinetic energy is conserved by conservation of energy.

An electron of charge ${-e}$ is accelerated through a potential difference of ${\Delta V = 5V}$. If it is initially at rest, what is the final speed ${v}$ the electron reaches after moving through the potential difference? \

At the start prior to motion, the electron would have potential energy. This potential energy is converted to kinetic energy as the electron traverses the potential difference.

Solving for ${v}$ gives us ${\rightarrow v = \sqrt{\frac{2e\Delta V}{m}}}$. Using the known quantities of ${e = 1.6 \cdot 10^{-19} \text{ C}}$ and ${m = 9.11 \cdot 10^{-31} \text{ kg}}$ gives us ${v = 1.3 \cdot 10^6 \text{ m/s}}$.

This is the whole idea of these problems. We simply note when energy is conserved and apply conservation of energy, relating potential energy to charge multiplied by potential difference and setting it equal to change in kinetic energy.