Hall Effect Calculator
Find Hall voltage V_H = BI/(nqt)
Parameters
Controls
Calculated Values
Examples
I=10 A, B=0.5 T
Copper-like n.
Visualization
Hall Effect
When current flows through a flat conductor in a magnetic field B perpendicular to the current, magnetic force deflects charge carriers to one side. Charge accumulation creates a transverse electric field (Hall field) until magnetic and electric forces on drifting carriers balance: qE_H = qv_d B.
The Hall voltage across thickness t is V_H = E_H × t = (v_d B) × t. Using current I = nqAv_d with cross-sectional area A = width × t gives the standard formula V_H = BI/(nqt), where n is carrier number density and q is carrier charge.
Sign of V_H reveals carrier type: electrons (negative q) give opposite Hall polarity to holes (positive q). Measuring V_H with known I, B, t, and n determines q or verifies semiconductor doping type.
Hall probes measure B by known geometry and calibration. Solid-state Hall sensors (GaAs, InSb) are in keyboards, brushless motor commutation, anti-lock braking wheel speed sensors, and phone flip covers.
In metals n is very large (~10²⁸ m⁻³) so V_H is tiny; semiconductors give larger, measurable V_H. Quantum Hall effect (2D electron gas, low T, high B) shows quantized V_H plateaus — fundamental constant measurement.
Example: I = 10 A, B = 0.5 T, t = 1 mm, n = 8.5×10²⁸ m⁻³ (copper-like) gives V_H on order 10⁻¹⁰ V — why Hall sensors use doped semiconductors instead.
Key Concepts
- V_H = BI/(nqt)
- Balance: qE_H = qv_d B
- Sign → electron vs hole
- Hall probe measures B
- n = carrier density
- Quantum Hall at extreme conditions
Real-World Applications
- Hall-effect magnetic sensors
- Brushless motor position
- Material carrier characterization
- Current transducers
- Automotive wheel speed
- Class 12 advanced reading
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Physics Equations
Step-by-Step Solution
See how the main results are calculated.
Step 1: Hall Effect Setup
Current I in slab, B perpendicular → Lorentz force deflects carriers.
Explanation:
Charge piles up on one face until Hall field balances magnetic force.
Step 2: Equilibrium Condition
Equation:
Explanation:
v_d = drift velocity of carriers.
Step 3: Hall Voltage Formula
Equation:
Explanation:
n = carrier number density, t = slab thickness, q = carrier charge.
Step 4: Substitute
Calculation:
Explanation:
Check units: (T·A)/(m⁻³·C·m) = V.
Step 5: Result
Calculation:
Result:
Step 6: Sign and Applications
Polarity reveals electron vs hole conduction.
Explanation:
Hall probes measure B; used in position sensors and smartphones.
Frequently Asked Questions (FAQ)
Metals vs semiconductors?
Semiconductors often larger Hall voltage due to lower n.
AC current?
Hall voltage follows I(t) and B(t) product.
Practice MCQs
- Hall voltage:
- Doubling B:
- Hall effect measures:
- Electrons in n-type semiconductor:
- Thicker sample t:
- Hall sensor advantage:
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