Conservation of Electric Energy
When a charge moves through a potential difference, ΔU_E=qΔV. If electric interaction is the only energy-transfer mechanism, the decrease in electric potential energy appears as an equal increase in kinetic energy.
Conservation of Electric Energy: quick answer
When a charge moves through a potential difference, ΔU_E=qΔV. If electric interaction is the only energy-transfer mechanism, the decrease in electric potential energy appears as an equal increase in kinetic energy. Potential difference becomes motion through energy conservation. The sign of q is decisive: moving to lower V lowers U for a positive charge but raises U for a negative charge. Draw an energy bar chart before calculating so the direction of kinetic-energy change is physically clear.
Define the system before writing an energy equation. If other forces, dissipation, external work or energy transfers are present, include them instead of forcing a two-term mechanical-energy equation.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at the worked examples.
Use ΔU_E=qΔV with correct signs.
Relate electric potential-energy change to kinetic-energy change when electric force is the only work interaction.
Use system boundaries and energy bar charts to include any additional transfers.
Predict charge motion or speed changes from potential maps without confusing potential with potential energy.
Key terms you need for this lesson
Definitions stay beside the model so a reader never has to leave the lesson to understand a prerequisite term.
electric potential-energy change
electric potential-energy change is the change ΔU_E=qΔV of the object–field interaction energy as a charge moves between two potentials.
kinetic-energy change
kinetic-energy change is the change in the moving object’s kinetic energy, equal to net work on the object.
energy conservation
energy conservation is the principle that total energy of an isolated system remains constant while energy changes form or is transferred between parts.
energy transfer
energy transfer is energy crossing the chosen system boundary through work, heating or other interactions.
energy bar chart
energy bar chart is a before/after representation that makes energy stores and transfer terms explicit.
electron volt
electron volt is an energy unit equal to the magnitude of energy change of one elementary charge moved through one volt: 1 eV=1.60×10⁻¹⁹ J.
Know what each relationship means and when it applies
The equation, variables, vector/scalar nature, model condition and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
ΔU_E = qΔV | ΔU_E electric potential-energy change of the object–field system (J); q moving charge (C); ΔV=V_f−V_i (V) | a charged object moves between two locations with known electric potentials | A positive charge moving to lower potential has ΔU_E<0; a negative charge has the opposite sign relation. |
ΔK = −ΔU_E = −qΔV | ΔK kinetic-energy change (J); ΔU_E electric potential-energy change (J) | electric force is the only force doing work and no other energy transfer crosses the chosen boundary | A released positive charge moving to lower potential gains kinetic energy equal to the electric potential-energy decrease. |
K_i + U_E,i = K_f + U_E,f | K kinetic energy (J); U_E electric potential energy (J) | closed conservative object–field system with no additional transfer terms | An electron accelerated through a potential difference can be analyzed by the same energy bookkeeping once the charge sign is handled correctly. |
What a strong diagram or graph must show
Translate the same physical model across words, diagrams, graphs and equations.
Potential map + charge sign
decide ΔV first, then use q to determine ΔU.
Energy bar chart
a drop in U_E becomes a rise in K when no other transfer occurs.
K-versus-position graph
can be inferred from conservation when total K+U_E is constant.
Trajectory reasoning
electric force direction comes from qE, while energy reasoning comes from qΔV; both descriptions must agree.
Change the model and inspect what must respond
Make a prediction first. Then move one control and explain the output using the governing relationship and representation.
Charge through a potential difference
Choose the charge sign and potential change. The tool calculates ΔU and the corresponding ΔK when electric force is the only work interaction.
Two examples with the model choice shown
The goal is to expose the reasoning pathway, not only the final number.
Proton through a potential drop
Situation: A proton moves from 500 V to 100 V and no other force does work.
Reasoning: ΔV=−400 V and q=+e, so ΔU=qΔV=−400 eV. Conservation gives ΔK=+400 eV.
The proton gains 400 eV of kinetic energy.
Electron sign check
Situation: An electron moves from 0 V to +250 V.
Reasoning: For q=−e and ΔV=+250 V, ΔU=qΔV=−250 eV. If electric force is the only work interaction, kinetic energy increases by 250 eV.
A negative charge can gain kinetic energy while moving toward higher electric potential because its potential-energy sign relation is opposite that of a positive charge.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 10.7?
Use electric-energy conservation when a charge moves through a potential difference and kinetic, electric potential, or external work terms change.
How this idea fits the course
This topic integrates 10.4 potential energy and 10.5 potential, and prepares the energy viewpoint used in circuit power and loop rules.
Scope check before solving
Define the system before writing an energy equation. If other forces, dissipation, external work or energy transfers are present, include them instead of forcing a two-term mechanical-energy equation.
Turn this topic into measurable evidence
A strong investigation identifies variables, controls competing causes, repeats trials and chooses a graph from the predicted functional dependence.
Investigation target
Use a charge-between-plates simulation to compare qΔV with measured kinetic-energy change.
Reasoning errors to eliminate
Repair the physical model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can define the core quantities and state whether each is vector or scalar.
- I can choose the governing relationship only after identifying source, probe and system boundary.
- I can explain every variable, unit, sign and reference convention.
- I can translate the situation into a field/equipotential/energy/geometry representation.
- I can predict direction or factor change before calculating.
- I can design or critique an experiment and justify a claim with data or physical principles.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 10.7 FAQs
What does qΔV represent?
It is the electric potential-energy change of a charge–field system when charge q moves through potential difference ΔV.
When is ΔK=−qΔV valid?
When electric force is the only force doing work and no additional energy transfer must be included.
Which way does a positive charge accelerate?
In the direction of E and, when released from rest under electric force alone, generally toward lower electric potential.
Which way does an electron accelerate?
Opposite E because its charge is negative; this is consistent with its potential energy decreasing as it moves toward higher V.
What is an electron volt?
1 eV is 1.60×10⁻¹⁹ J, the energy magnitude associated with moving one elementary charge through 1 V.
Why define the system first?
The system choice determines whether electric potential energy is inside the system and whether external work or other transfers must appear explicitly.