To investigate the magnetic dipole field generated by permanent bar magnets along the axial End-on (Tan-A) position of Gauss, verify the inverse-cube magnetic field distance dependence (B ∝ 1/d³), determine the magnetic dipole moment (M) and the ratio of moments using ordinary least-squares linear regression, and compare deflection and oscillation methods for geomagnetic metrology. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
The theoretical model treats the magnetic needle as an infinitesimal point dipole situated at the exact geometric center of the bench, assumes the bar magnet acts as an ideal point dipole (neglecting finite magnetic length corrections (d² − ℓ²)² which contribute ~0.5% at closest approach d = 14 cm), and treats Earth's magnetic field as strictly stationary and uniform. In a physical laboratory, building structural steel reinforcement produces localized geomagnetic distortion, pivot jewel stiction introduces a ±0.2° dead-zone threshold, and diurnal geomagnetic drift causes minor baseline fluctuations (~0.1 μT).
Rigid 1-meter non-magnetic mahogany optical bench with dual millimeter scales, leveling tripod screws, and central circular compass box with 360° protractor scale, anti-parallax mirror ring, and jewel-pivoted needle.
Precision cylindrical permanent magnet (length 2L = 10.0 cm, diameter 8.0 mm, dipole moment M₁ = 0.8750 A m²) for primary inverse-cube field mapping and slope regression.
Matched cylindrical permanent magnet of lower magnetization (M₂ = 0.5250 A m²) for evaluating magnetic moment ratios (M₁ / M₂) across identical distance stations.
Non-magnetic brass sliding carriage equipped with vernier index cursor, thumbscrew lock, and dual orientation V-blocks for rapid, repeatable magnet positioning and 180° axial reversal.
Draft-free glass-walled oscillation chamber with unspun silk fiber suspension and torsion head for measuring the magnet's torsional oscillation period T in Earth's field.
Quartz digital timer (0.01 s resolution) for oscillation timing and vernier calipers (0.02 mm resolution) for measuring magnet physical dimensions to compute moment of inertia.
To investigate the magnetic dipole field generated by permanent bar magnets along the axial End-on (Tan-A) position of Gauss, verify the inverse-cube magnetic field distance dependence (B ∝ 1/d³), determine the magnetic dipole moment (M) and the ratio of moments using ordinary least-squares linear regression, and compare deflection and oscillation methods for geomagnetic metrology. Suggested independent settings: 14.0, 16.0, 18.0, 20.0, 22.0, 24.0 cm.
Place the deflection magnetometer on a rigid non-magnetic bench far from ferromagnetic fixtures or DC power leads. Using the brass leveling screws, level the instrument until the compass needle swings freely. Rotate the entire bench until the long aluminum pointer reads exactly 0°–0° while the arms of the bench extend precisely East and West.
This alignment guarantees that the bar magnet's axial field along the bench is strictly perpendicular to Earth's horizontal geomagnetic field, satisfying the tangent law.
Measure the physical length 2L and diameter of Magnet 1 using vernier calipers, and weigh it on an analytical balance. Calculate the effective magnetic length between pole centers using the standard empirical relation 2ℓ = 0.84 × 2L = 8.40 cm.
Accurate physical dimensions are necessary to evaluate finite-length multipole corrections (d² − ℓ²) and compute moment of inertia.
Place Magnet 1 on the East arm carrier at distance d = 14.0 cm with its North pole facing inward toward the compass needle. Read both ends of the aluminum pointer (θ₁ and θ₂) using the anti-parallax mirror. Reverse the magnet on the carrier so its South pole faces inward, and record both ends (θ₃ and θ₄).
Averaging both pointer ends cancels pivot eccentricity, while reversing magnet polarity cancels residual pointer bending offsets.
Transfer the magnet carrier to the West arm at the exact same distance d = 14.0 cm. Repeat the dual-polarity measurement sequence (North inward, then South inward), recording both pointer ends (θ₅, θ₆, θ₇, θ₈). Compute the grand mean deflection θ = (Σ θ_i) / 8.
Testing both East and West arms cancels out any slight mechanical asymmetry in scale indexing or residual leveling tilt.
Repeat the complete eight-reading measurement sequence for six discrete distances (d = 14.0, 16.0, 18.0, 20.0, 22.0, and 24.0 cm). For each distance, compute the inverse-cube variable x = 1 / d³ (in m⁻³) and the dependent variable y = tan θ.
Varying distance over the optimum angular window (20° to 61°) provides robust data for linear regression, confirming the inverse-cube dipole law.
Replace Magnet 1 with Magnet 2 and record deflections at identical distances. Compute the ratio of magnetic moments M₁ / M₂ = tan θ₁ / tan θ₂ to verify relative magnetization independent of Earth's field B_H.
Comparing two magnets at identical distances isolates their moment ratio directly, canceling out the geomagnetic field B_H.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Magnet distance d (cm) | Compass deflection angle θ (°) | Inverse-cube distance 1/d³ (m⁻³) | Tangent of deflection (tan θ) | Remove |
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