Sideways charge separation creates a voltage
You will be able to: Explain Hall charge separation and the electric–magnetic force balance on charge carriers.
How can a magnetic field create a transverse voltage in a conductor?
Electrons drift right through a strip while B points out of the page. Magnetic force pushes the electrons upward. The top becomes more negative and the bottom more positive, building an upward electric field that pushes negative electrons back down.
A useful starting point: Balance electric and magnetic forces →
Words and symbols before equations
- Hall voltage
- Potential difference across the width of a current-carrying conductor in a transverse magnetic field.
- Charge carrier
- Particle carrying the current; this lesson explicitly models negative electrons.
- Transverse
- Across the strip, perpendicular to the drift direction.
- Equilibrium
- Sideways electric and magnetic forces balance after a small charge separation.
What this picture assumes
Negative carriers drift right. |B|=0.50 T, strip width 0.020 m. Charge separation and arrows are exaggerated. The equilibrium calculation neglects complications of real Hall sensors.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- B out of page. Top becomes negative; E_H points up, opposite the electron electric force. |V_H|=0.1 mV.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Use actual carrier velocity and charge sign. For rightward electron drift and outward B, v×B is downward for a positive charge, so the electron magnetic force is upward. Electrons accumulate slightly at the top surface.
The resulting electric field points upward from the positive bottom toward the negative top. The force qE on electrons is therefore downward and balances the upward magnetic force.
At transverse equilibrium, E_H=v_d B in this perpendicular idealized model, and voltage magnitude is E_H times strip width. The microscopic separation is tiny; the diagram exaggerates it. Hall polarity can reveal carrier sign when current and field directions are known.
A worked example, step by step
Electrons drift right at 0.010 m/s in B=0.50 T out of the page. The strip width is 0.020 m. Find Hall voltage magnitude and polarity.
- Electron magnetic force is upward, so the top becomes negative.
- The balancing E field points upward; negative electrons feel downward electric force.
- E_H=v_d B=0.0050 N/C.
- |ΔV_H|=E_H w=0.00010 V=0.10 mV; bottom is at higher potential than top.
Electron velocity is opposite conventional current. Keep the chosen carrier direction explicit before applying the right-hand rule.
Does an upward electric field push an electron upward?
Compare with an explanation
No. Negative charge makes its electric force downward.
Predict. Change one thing. Explain.
Reverse B while retaining rightward electron drift. Predict which surface becomes negative, the electric field direction and the higher-potential side.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
B out of page. Top becomes negative; E_H points up, opposite the electron electric force. |V_H|=0.1 mV.
Negative carriers drift right. |B|=0.50 T, strip width 0.020 m. Charge separation and arrows are exaggerated. The equilibrium calculation neglects complications of real Hall sensors.
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 questionFor electrons drifting right in outward B, (a) state magnetic force direction, (b) identify the negative side, (c) state induced electric field direction, and (d) state electric force direction on electrons.
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Compare with the answer and four-point rubric
- 1 point: Magnetic force up.
- 1 point: Top becomes negative.
- 1 point: Electric field points up from positive bottom toward negative top.
- 1 point: Electric force on electrons is down, balancing magnetic force.
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 1What causes the Hall voltage?
A small transverse redistribution of carriers driven by magnetic force.
RECALL 2Is E directed from negative to positive?
No. Electric field points from higher toward lower potential: positive toward negative in this strip.
RECALL 3What balances the carrier’s sideways magnetic force?
The electric force due to the separated charges.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Sideways charge separation creates a voltage
- At perpendicular carrier equilibrium: |E_H|=v_d B.
- Uniform transverse field: |ΔV_H|=|E_H|w.
- Hall polarity depends on carrier sign and motion.
Remember: Electron velocity is opposite conventional current. Keep the chosen carrier direction explicit before applying the right-hand rule.
Conditions: Negative carriers drift right. |B|=0.50 T, strip width 0.020 m. Charge separation and arrows are exaggerated. The equilibrium calculation neglects complications of real Hall sensors.
Refresh Kid · AP Physics 2 Unit 4 (official Unit 12) · Objectives 12.2.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 12.2, objectives 12.2.B. 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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