Stewart & Gee Tangent Galvanometer
Precision instrument with 50-turn vertical circular copper coil (mean radius R = 10.0 cm), brass leveling tripod with leveling screws, and central compass box with 360° protractor scale and anti-parallax mirror.
Physics / Magnetic Fields & Tangent Galvanometer
FREE TO EXPLOREEXPERIMENT 44 · PHYSICS LABORATORY
Magnetic Fields: Tangent Galvanometer, Biot-Savart Law, and Earth's Horizontal Magnetic Component
To investigate the magnetic field generated by an electric current in a circular coil, verify the Biot-Savart law and tangent law of magnetism, observe magnetic torque equilibrium on a compass needle, and determine the horizontal component of Earth's magnetic field (B_H) and the reduction factor using linear regression. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
COMPASS DEFLECTION ANGLE Θ—
MEASUREMENT STATUS
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.
Simulation assumptions and limits
The analytical model treats the magnetic needle as an infinitesimal point dipole situated at the exact geometric center of the circular coil, assumes perfectly uniform coil windings with negligible axial width, and treats Earth's magnetic field as strictly stationary and uniform. In a physical laboratory, finite needle length introduces a small second-order correction (1 + 0.75 (ℓ/R)² (5 cos² θ − 1) ≈ 0.2%), building structural steel reinforcement produces localized geomagnetic distortion, and diurnal solar geomagnetic drift causes minor baseline fluctuations (~0.1 μT).
Know your apparatus.
Pohl Current Reversing Commutator
Heavy-duty four-terminal rocker commutator allowing rapid, arc-free reversal of current direction through the galvanometer coil without disturbing circuit connections.
Regulated DC Power Supply
Low-noise variable DC voltage supply (0 to 12.0 V, 2 A) equipped with digital voltage and current monitoring.
Precision Decade Resistance Box / Slide-Wire Rheostat
Non-inductive wire-wound rheostat (0 to 100 Ω, 2 A rating) for smooth, continuous adjustment of coil current.
Digital Multimeter / Precision Ammeter
Calibrated 4½-digit true-RMS digital ammeter (0.1 mA resolution) to verify current readings against galvanometer deflections.
Magnetic Dip Needle and Compass
Freely suspended dip circle for determining the local magnetic meridian and measuring inclination angle.
FOLLOW THE METHOD
A reason behind every step.
To investigate the magnetic field generated by an electric current in a circular coil, verify the Biot-Savart law and tangent law of magnetism, observe magnetic torque equilibrium on a compass needle, and determine the horizontal component of Earth's magnetic field (B_H) and the reduction factor using linear regression. Suggested independent settings: 50.0, 80.0, 110.0, 140.0, 170.0, 200.0 mA.
Leveling and Magnetic Meridian Alignment
Place the tangent galvanometer on a rigid, non-magnetic wooden bench away from iron fixtures or DC power leads. Using the leveling screws, level the base until the central compass needle swings freely. Rotate the coil until its vertical plane is exactly parallel to the compass needle pointing North-South (0°–0° alignment).
Why this step matters
The tangent law B_coil = B_H tan θ requires the coil's axial magnetic field to be strictly orthogonal to Earth's horizontal field.
Circuit Wiring and Commutator Connection
Connect the DC power supply in series with the rheostat, precision ammeter, reversing commutator, and the 50-turn coil terminals. Inspect all connections to verify tight, clean non-magnetic contacts.
Why this step matters
Series connection ensures identical current flows through the ammeter and galvanometer coil, while the commutator enables bilateral deflection testing.
Current Adjustment and Forward Deflection Recording
Turn on the power supply and adjust the rheostat until a current of I = 50.0 mA flows through the coil. Using the anti-parallax mirror (aligning the pointer with its image), record the deflection angle θ1 on both ends of the aluminum pointer (East and West tips).
Why this step matters
Reading both ends of the pointer eliminates error caused by the pointer pivot not being at the exact center of the graduated scale.
Commutation and Reversed Deflection Recording
Throw the reversing commutator to reverse the current direction through the coil without altering the rheostat. Record the deflection angle θ2 at both ends of the pointer on the opposite side of the scale, and calculate the mean deflection θ = (θ1 + θ2) / 2.
Why this step matters
Reversing current cancels out zero-offset pointer bending, residual coil tilt, and minor magnetic meridian alignment errors.
Systematic Current Variation
Repeat the four-reading measurement sequence for six discrete current levels (50.0, 80.0, 110.0, 140.0, 170.0, and 200.0 mA). Record current I in mA and calculate tan θ for each station.
Why this step matters
Varying current over the optimum deflection range (24° to 61°) provides robust data for linear regression, yielding an accurate slope.
Coil Dimension Verification
Measure the inner and outer diameters of the circular coil using vernier calipers to compute the mean radius R = 10.0 cm, and confirm the turn count N = 50.
Why this step matters
Accurate knowledge of coil geometry is essential to calculate the coil constant G = μ₀ N / (2R) and isolate Earth's horizontal field B_H.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
\tan\theta = \left(\frac{\mu_0 N}{2 R B_H}\right) I \iff y = m x + b \iff B_H = \frac{\mu_0 N}{2 R m}, \quad K = \frac{1}{m}
| # | Direct coil current I (mA) | Compass deflection angle θ (°) | Coil current I | Tangent of deflection (tan θ) | Remove |
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