Conservation of Electric Energy
A charge in a field is like a ball on a hill
- Release a ball on a slope and it speeds up, trading height for speed.
- Release a charge in an electric field and it does the same, trading electric potential energy for kinetic.
- The two energies swap, but their total never changes.
- Energy conservation, which we met for gravity, works just as well for charges.
PE and KE trade off
- A charge moving through a field converts electric PE into kinetic energy (or back).
- $U + \tfrac12 mv^2 = \text{constant}$ for a charge with no other forces.
- Let a positive charge be repelled: its PE falls and it speeds up.
- Push it against the field: its speed drops and its PE rises.
As a positive charge is repelled and speeds up, its electric potential energy:
PE falls as it converts into kinetic energy; the total stays constant.
For a charge with no other forces, electric PE plus ____ energy is constant.
$U + \tfrac12 mv^2 = \text{constant}$ — PE and kinetic energy trade off.
Using voltage to find speed
- The energy a charge gains crossing a voltage $\Delta V$ is $W = q\,\Delta V$.
- All of it can become kinetic energy: $q\,\Delta V = \tfrac12 m v^2$.
- This is exactly how particle accelerators speed up electrons and protons.
- Bigger voltage or bigger charge means a faster final speed.
A $2\ \text{C}$ charge accelerates from rest through $9\ \text{V}$. How much kinetic energy does it gain, in $\text{J}$?
$\text{KE} = q\Delta V = 2 \times 9 = 18\ \text{J}$.
Particle accelerators use a voltage to convert electric potential energy into kinetic energy of charges.
A charge gains $q\Delta V$ of kinetic energy crossing the voltage — how accelerators work.
The same toolkit as mechanics
- Conservation of energy links the start and end without tracking the messy middle.
- Set total energy at the start equal to total energy at the end, and solve.
- It unifies electricity with all the mechanics energy tools you already know.
- Whenever forces are conservative (gravity, springs, electric), this shortcut works.
Charge gaining or losing kinetic energy
As a charge moves through a field, energy shifts between kinetic and potential. Sort each case.
Select all true statements about a charge moving freely in an electric field.
Energy is conserved (traded, not created); crossing $\Delta V$ transfers $q\Delta V$.
Conservation of energy applies only when no energy leaks away (no friction or resistance stealing it). In a circuit, resistors turn electrical energy into heat, so there the energy is conserved overall but not stored as kinetic — track where it goes.
In a circuit, why isn't all the electrical energy turned into kinetic energy?
Resistors convert electrical energy to heat, so energy is conserved overall but not stored as motion.
A charge of $q = 2\ \text{C}$ is accelerated from rest through a potential difference of $\Delta V = 9\ \text{V}$. How much kinetic energy does it gain?
- $\text{KE} = q\,\Delta V = 2 \times 9 = 18\ \text{J}$.
All the electric potential energy it loses reappears as kinetic energy.
Conservation of electric energy: a charge trades electric potential energy for kinetic energy with the total unchanged, $U + \tfrac12 mv^2 = \text{constant}$. Crossing a voltage, it gains $W = q\,\Delta V$ — how accelerators work. It is the same energy toolkit as mechanics.