Account for the energy in a generator
You will be able to: Balance pulling power with resistive heating in an ideal sliding-rod generator and design a controlled comparison.
Where does induced electrical energy come from?
Keep pulling the rail-mounted rod at steady speed. Its induced current experiences a magnetic force opposing the motion. Your pulling force supplies mechanical energy that becomes electrical heating in the circuit.
A useful starting point: A moving rod separates charge →
Words and symbols before equations
- Magnetic drag
- Force on the current-carrying rod opposite its motion in this setup.
- Steady speed
- No change in rod kinetic energy; applied force balances drag when other forces are neglected.
- Mechanical power
- Rate of work by the pulling force, P=Fv.
- Resistive power
- Electrical heating rate I²R.
What this picture assumes
B=0.50 T into page, rod length 0.40 m, constant speed held by an external pull. Closed resistive rails, no friction or self-inductance. Emf–speed graph is an ideal prediction, not experimental data.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- ε=0.6 V; I=0.3 A; drag=0.06 N left. At steady speed, pull power=0.18 W equals resistor heating=0.18 W. Graph slope BL=0.20 V/(m/s).
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
For the closed perpendicular rail circuit, ε=BLv and I=BLv/R. Force on the rod has magnitude F_B=ILB and points against motion. To maintain constant speed with no friction, external pulling force equals that drag.
Then P_pull=Fv=(ILB)v=Iε=I²R. Energy comes from the external agent, not from a static magnetic field doing work on individual charges. Magnetic forces redirect charge motion and transmit the interaction; the complete energy account includes the mechanically driven conductor.
A test can vary v at fixed B, L and R and compare measured emf with speed. Plot ε vertically against v horizontally: slope should be BL. Record uncertainties and repeat trials. The Explore values are ideal predictions, not measured data; neglect friction and self-inductance.
A worked example, step by step
For B=0.50 T, L=0.40 m, v=3 m/s and R=2 Ω, compare pulling power and heating.
- ε=BLv=0.60 V and I=ε/R=0.30 A.
- Drag magnitude F=ILB=(0.30)(0.40)(0.50)=0.060 N.
- Steady pulling power Fv=(0.060)(3)=0.18 W.
- Heating I²R=(0.30)²(2)=0.18 W, exactly matching the input.
Induction does not supply energy from nowhere. Include the work needed to maintain the changing-flux process.
Double v in this fixed-R model. What happens to power?
Compare with an explanation
Emf and current double, so I²R and pulling power quadruple.
Predict. Change one thing. Explain.
Change speed at fixed B, L and R. Predict how emf, drag and power scale. Compare input and output powers and the synthetic ε–v graph.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
ε=0.6 V; I=0.3 A; drag=0.06 N left. At steady speed, pull power=0.18 W equals resistor heating=0.18 W. Graph slope BL=0.20 V/(m/s).
B=0.50 T into page, rod length 0.40 m, constant speed held by an external pull. Closed resistive rails, no friction or self-inductance. Emf–speed graph is an ideal prediction, not experimental data.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant field, force, flux or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA rod generator has B=0.20 T, L=0.50 m, v=4 m/s and R=2 Ω. (a) Find emf and I. (b) Find drag. (c) Find pulling power. (d) Check heating power.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: ε=0.40 V and I=0.20 A.
- 1 point: F=ILB=0.020 N.
- 1 point: P_pull=Fv=0.080 W.
- 1 point: I²R=0.080 W, matching the input.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Why does the rod require a pull at constant speed?
Induced current creates magnetic drag opposing its motion.
RECALL 2Which graph tests ε proportional to v?
Emf versus speed, with B, L and R controlled.
RECALL 3What is the energy source in the ideal rod generator?
Mechanical work supplied by the pulling agent.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Account for the energy in a generator
- ε=BLv; I=ε/R.
- Magnetic drag magnitude F=ILB.
- Steady ideal pulling: Fv=Iε=I²R.
Remember: Induction does not supply energy from nowhere. Include the work needed to maintain the changing-flux process.
Conditions: B=0.50 T into page, rod length 0.40 m, constant speed held by an external pull. Closed resistive rails, no friction or self-inductance. Emf–speed graph is an ideal prediction, not experimental data.
Refresh Kid · AP Physics 2 Unit 4 (official Unit 12) · Objectives 12.4.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 12.4, objectives 12.4.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the fourth AP Physics 2 unit; College Board numbers it Unit 12; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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