Explain the Hall effect and measure magnetic flux density
Trace charge separation in a current-carrying conductor, derive the Hall-voltage relation and use a Hall probe.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 20. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use current, charge, force, velocity, vectors, area and SI units; distinguish conventional current from electron flow.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What creates the Hall voltage in a current-carrying strip in a magnetic field?
What you will learn
- Explain the origin of Hall voltage
- Derive and use V_H = BI/(ntq)
- Explain how a Hall probe measures magnetic flux density
Magnetic force separates charge carriers
In a current-carrying strip placed in a magnetic field, moving charge carriers experience a sideways magnetic force. Charge accumulates on opposite sides until the electric force from the separation balances the magnetic force. The resulting transverse potential difference is the Hall voltage V_H.
For carrier number density n, strip thickness t in the field direction, current I and carrier charge magnitude q, the Hall relation is V_H = BI/(ntq). This form uses magnitudes; the Hall-voltage polarity also carries information about the sign of the dominant charge carriers.
A Hall probe uses the voltage as a field signal
A calibrated Hall probe uses a Hall element and measures its transverse voltage. If I, n, t and q are known, rearrange B = V_Hntq/I to find magnetic flux density. The probe must be oriented consistently because the signal depends on the component of field perpendicular to the current and carrier motion.
Increasing B or I increases Hall-voltage magnitude; increasing carrier density, thickness or carrier-charge magnitude reduces it under this model. Check the unit result for B is tesla.
Pause and explain
If B and I double while n, t and q stay fixed, what happens to |V_H|?
Worked example
A Hall element has V_H = 0.20 V, n = 5.0 × 10²⁰ m⁻³, t = 0.50 mm, q = 1.6 × 10⁻¹⁹ C and I = 0.010 A. Find B.
Show the worked solution
- Convert t = 0.50 mm to 5.0 × 10⁻⁴ m.
- Use B = V_Hntq/I.
- Substitute values and give teslas.
Answer B = (0.20)(5.0 × 10²⁰)(5.0 × 10⁻⁴)(1.6 × 10⁻¹⁹)/0.010 = 0.80 T.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A Hall voltage is 0.12 V for I = 0.015 A, n = 4.0 × 10²⁰ m⁻³, t = 0.40 mm and q = 1.6 × 10⁻¹⁹ C. Calculate B.
Give me a hint
Convert thickness to metres and rearrange for B.
Compare my reasoning
- t = 4.0 × 10⁻⁴ m.
- B = V_Hntq/I.
- B = (0.12)(4.0 × 10²⁰)(4.0 × 10⁻⁴)(1.6 × 10⁻¹⁹)/0.015 ≈ 0.205 T.
B ≈ 0.21 T.
Look for these in your work
- Thickness converted
- Relation rearranged
- Field strength calculated
At fixed B, n, t and q, the current in a Hall element is reduced by a factor of three. How does the Hall-voltage magnitude change?
Give me a hint
Use the direct proportionality V_H ∝ I.
Compare my reasoning
- All other quantities are fixed.
- V_H is directly proportional to I.
- Reducing I to one third reduces |V_H| to one third.
The Hall-voltage magnitude becomes one third of its original value.
Look for these in your work
- Fixed quantities identified
- Proportionality used
- Ratio stated
Explain how a Hall probe can map the field near the pole of a magnet and why orientation matters.
Give me a hint
Relate measured Hall voltage to the field component and probe calibration.
Compare my reasoning
- Place the Hall element at a point and read its transverse voltage.
- Use calibration or B = V_Hntq/I to infer the perpendicular field component.
- Keep probe orientation controlled because rotating it changes the component and possibly the polarity.
The calibrated Hall voltage gives the local field component; controlled orientation ensures the reading corresponds to the intended direction.
Look for these in your work
- Voltage measured
- Field inferred
- Orientation effect explained
Common mistakes
- Treating Hall voltage as along the current rather than transverse
- Using thickness in millimetres without converting
- Dropping the carrier charge magnitude from the relation
- Ignoring Hall-voltage polarity when identifying carrier sign
What can you explain now?
What creates the Hall voltage in a current-carrying strip in a magnetic field?
Compare with the explanation
Sideways separation of moving charge carriers
The magnetic force pushes carriers towards opposite sides.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
How does magnetic force create a Hall voltage, and what does a Hall probe measure?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.