Interactive practical

Magnetic flux density using a Hall probe

Zero a Hall probe, measure the flux density at the centre of a solenoid for five currents and along its axis, then estimate μ₀ from the B–I gradient and compare the field at the end with the centre.

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A-Level Physics

Magnetic flux density using a Hall probe

WJEC 1420QS — matched to your course.

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Practical focus

Use a Hall probe to map and measure magnetic flux density.

Practical method

Aim

Use a Hall probe to measure the magnetic flux density inside a solenoid and investigate how it depends on current.

Variables

Independent variable: current in the solenoid
Dependent variable: flux density B at the centre
Control variables: position and orientation of the probe; the same solenoid (turns per metre).

Apparatus

Long solenoid (2000 turns per metre)
Variable d.c. supply and ammeter
Calibrated Hall probe and meter (or data logger)

Method

Zero the Hall probe away from magnets, with no current in the solenoid.
Place the probe at the centre of the solenoid with its flat face perpendicular to the axis.
Record B for currents from 0.5 A to 2.0 A.
Reverse the current and repeat; average the magnitudes to cancel the Earth's field.
Plot B against I and compare the gradient with μ₀n.

Sample results

Solenoid with n = 2000 turns per metre.

I / A	B / mT
0.5	1.26
1.0	2.51
1.5	3.77
2.0	5.03

Analysis

B is proportional to I with gradient 2.51 × 10⁻³ T A⁻¹. Dividing by n gives μ₀ = \(\dfrac{2.51 \times 10^{-3}}{2000}\) = 1.26 × 10⁻⁶ T m A⁻¹, matching 4π × 10⁻⁷.

Uncertainty

The probe must be perpendicular to the field: a 5° tilt reduces the reading by under 0.5%. The Earth's field (about 0.05 mT) matters only at low currents; reversing the current removes it.

Errors and improvements

Problem	Effect	Improvement
Probe not perpendicular to the field	Reading too low	Rotate the probe to find the maximum
Earth's field and stray fields	Offset in readings	Zero the probe; reverse current and average
Probe off the axis or near the ends	Field not uniform	Keep the probe at the centre

Risk assessment

Hazard	Risk	Control measure
Solenoid heating at high current	Burns	Switch off between readings
Delicate probe	Damage	Handle carefully

Common mistakes

Holding the probe parallel to the field.
Forgetting to zero the probe.
Placing the probe near the ends of the solenoid.

Worked analysis

At 1.5 A: B = μ₀nI = 4π × 10⁻⁷ × 2000 × 1.5 = 3.77 × 10⁻³ T = 3.77 mT, matching the measurement.

Common misconception

A Hall probe measures only the component of B perpendicular to its sensing face, so orientation matters.

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Practical 2

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