20.3.4Magnetic fields and alternating currents (A Level)
Using a Hall Probe
5 min read 10 parts Lesson 9 of 24 1 quiz
Lesson summary
20.3.4 Using a Hall Probe — AS PHYSICS 9702 notes: Describe how a Hall probe is calibrated and used to measure magnetic flux density.Hall probe — a flux density meter with a small semiconductor wafer at its tip carrying a constant currentConnection — two contacts on opposite edge…
- Sensitivity
- Plot VH against B
- Digital instruments
- Perpendicular component
- Tilted probe
- Direction of the field
Section 1 of 10What a Hall probe is
Hall probe
- Hall probe a flux density meter with a small semiconductor wafer at its tip carrying a constant current
Connection
- Connection two contacts on opposite edges of the wafer are connected to a sensitive voltmeter reading VH
Principle
- VH = BI/(ntq), and I, n, t and q are fixed, so VH = kB with k = I/(ntq)
Sensitivity
- Sensitivity it can measure even the Earth's magnetic flux density
Section 2 of 10Calibration
Place the probe in a field of known size, such as the centre of a long solenoid or between standard magnet poles
Record VH for a series of known fields
Plot VH against B
- Plot VH against B a straight line through the origin with gradient k
Convert an unknown reading to B by dividing by k or reading off the line
- Digital instruments
- they convert internally and display B in mT directly
Section 3 of 10Orientation of the probe
Orientation of the probe
Perpendicular component
- Perpendicular component only the component of B perpendicular to the face of the wafer gives a Hall voltage
Tilted probe
- Tilted probe if the field makes an angle φ with the plane of the wafer, the reading is proportional to B sin φ
Extremes
- Extremes zero when the wafer is parallel to the field and maximum when it is perpendicular
Finding B
- Finding B rotate the probe until the voltage is greatest, and the reading is B itself
Direction of the field
- Direction of the field the reading drops to zero when the probe plane lies along the lines
Between magnets
- Between magnets hold the flat face between the poles so the field passes perpendicular to it
Section 4 of 10Zeroing and practical points
Zero error
- Zero error with no field the voltmeter might show a small reading because the Hall contacts are not exactly opposite
- Record it and subtract it from every reading
Keep the probe still
- Keep the probe still small movements change position and angle
Point sampling
- Point sampling the probe measures the field only over its small wafer, good for mapping along a line
Same current
- Same current use the same current for calibration and measurement and keep it small to avoid heating, which changes n
Section 5 of 10Comparing with other methods
Search coil
- Search coil gives an e.m.f. proportional to the rate of change of flux and needs a changing field
Current balance
- Current balance measures the average field across a wire length and is cumbersome
Hall probe
- Hall probe measures a steady field at a point with an instant reading, the standard choice for mapping a static field
Section 6 of 10Accuracy
Resolution
- Resolution limited by the wafer size and voltmeter noise
- (a few millimetres)
Accuracy
- Accuracy depends on calibration, temperature and alignment
- (carrier density changes)
Reducing random error
- Reducing random error take repeated readings at each position and average
Locating a field line
- Locating a field line rotate the probe to find the position where the reading drops to zero, then turn it through 90°
Misalignment
- Misalignment a probe tilted from the ideal orientation always under-reads the true flux density
Section 7 of 10Typical uses
Mapping fields
- Mapping fields along a solenoid axis, in a magnet gap or around a straight wire
Solenoid check
- Solenoid check a graph of B against current is a straight line through the origin
Other uses
- Other uses the Earth's field and position sensors in car crankshafts, brushless motors and phone compasses
Why it works
- Why it works all rely on VH ∝ B
Section 8 of 10More from the specification
More from the specification
Hall effect and magnetic forces
- Hall effect and magnetic forces perpendicular magnetic fields exert transverse magnetic forces on mobile charge carriers, balancing electrostatic forces.
Magnetic Lorentz force on a moving charge
- A charged particle carrying charge q moving with velocity v at an angle theta to a magnetic field B experiences a magnetic deflection force given by F = B q v sin(theta).
Fleming's left-hand rule
- Fleming's left-hand rule determines the direction of magnetic force on a moving charge: Thumb represents Force, First finger represents magnetic field B,
- and seCond finger represents conventional current.
- (opposite to electron velocity for negative charges)
The Hall effect mechanism
- When current flows through a semiconductor slice in a perpendicular magnetic field, moving electrons experience magnetic deflection towards one face, creating charge separation and a transverse electric field.
Hall voltage and magnetic field measurement
- Equilibrium between magnetic force (FB = Bqv) and electric force (FE = qE_H) generates a stable Hall voltage VH = B I / (n t q),
- where VH is directly proportional to magnetic flux density B, calibrated to measure field strength with a Hall probe.
Magnetic Lorentz force on a moving charge
- A charged particle carrying charge q moving with velocity v at an angle theta to a magnetic field B experiences a magnetic deflection force given by F = B q v sin(theta).
Fleming's left-hand rule
- Fleming's left-hand rule determines the direction of magnetic force on a moving charge: Thumb represents Force, First finger represents magnetic field B,
- and seCond finger represents conventional current.
- (opposite to electron velocity for negative charges)
The Hall effect mechanism
- When current flows through a semiconductor slice in a perpendicular magnetic field, moving electrons experience magnetic deflection towards one face, creating charge separation and a transverse electric field.
Hall voltage and magnetic field measurement
- Equilibrium between magnetic force (FB = Bqv) and electric force (FE = qE_H) generates a stable Hall voltage VH = B I / (n t q),
- where VH is directly proportional to magnetic flux density B, calibrated to measure field strength with a Hall probe.
Uniform
- Same density throughout, so the weight acts at the centre.
Radius
- Distance from the centre to the circular path.
Field strength
- G = Fg/m.
Magnetic force
- The force on a moving charge in a magnetic field
Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Velocity
- Rate of change of displacement.
Electron
- Negatively charged particle in an atom.
F = BQv
What the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s−1)
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Hall probe | a meter using the Hall voltage of a semiconductor wafer to measure B |
| Calibration | comparing readings with known fields to find the constant k |
| Zero error | a non-zero reading with no field present |
| Search coil | a coil giving an e.m.f. from a changing flux |
| Resolution | the smallest change in B that can be detected |
| Flux density | B, the measure of magnetic field strength in tesla |
Section 10 of 10Exam technique
1
Reading the probe at an angle and assuming it is B — rotate to find the maximum.
2
Ignoring the zero error — subtract it from every reading.
3
Saying a tilted probe over-reads — it under-reads.
4
Using a different current for calibration and measurement — keep it the same.