Coulomb Torsion Balance
Precision electrostatic torsion balance housed in a draft-free cylindrical glass chamber with circular degree vernier scale, grounded conductive floor, and low-torsion phosphor bronze suspension fiber.
Physics / Electrostatics & Coulomb's Law
FREE TO EXPLOREEXPERIMENT 43 · PHYSICS LABORATORY
Electrostatics: Coulomb's Law, Electric Induction, and Charge Quantification
To investigate electrostatic charge production by friction and induction, verify Faraday's ice-pail experiment and charge conservation, measure the electrostatic force between charged spheres as a function of distance using a Coulomb torsion balance, confirm the inverse-square law, and determine Coulomb's constant and the permittivity of free space using linear regression. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
ELECTROSTATIC FORCE F—
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 conducting spheres as mathematical point charges in an infinite, unbounded vacuum, neglecting electrostatic image charges induced in the chamber walls, minor finite-size multipole surface charge redistribution (Lord Kelvin image correction ~0.3% at r = 4 cm), and residual atmospheric ion leakage (~0.1 nC/min). In a physical laboratory, slight fiber mechanical hysteresis (zero drift after large twists), minute convective air currents inside the glass chamber, and environmental humidity fluctuations introduce small experimental scatter.
Know your apparatus.
Matched Conducting Spheres
Pair of precision-turned, lightweight gold-plated conducting spheres (radius a = 5.0 mm), one suspended on an insulating dielectric balance arm and the other mounted on a graduated sliding carrier.
Regulated High-Voltage DC Source
Continuously variable low-current power supply (0 to 6.0 kV DC, 50 μA current-limited) for depositing calibrated electrostatic charges on the conducting spheres.
Precision Proof Plane and Faraday Ice Pail
Polished metallic proof plane disc with amber insulating handle and an insulated nickel-plated Faraday ice pail connected to a digital electrometer for quantitative charge sampling.
Gold-Leaf Electroscope
Enclosed glass-windowed electroscope with grounded metal shielding case, calibrated leaf divergence protractor, and high-insulation sulfur bushing.
Desiccated Environmental Chamber
Hermetically sealed chamber enclosure with rechargeable silica gel desiccant column to maintain relative humidity below 25%, preventing atmospheric ion leakage.
FOLLOW THE METHOD
A reason behind every step.
To investigate electrostatic charge production by friction and induction, verify Faraday's ice-pail experiment and charge conservation, measure the electrostatic force between charged spheres as a function of distance using a Coulomb torsion balance, confirm the inverse-square law, and determine Coulomb's constant and the permittivity of free space using linear regression. Suggested independent settings: 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 cm.
Chamber Preparation and Environmental Desiccation
Inspect the torsion balance glass chamber and verify that the internal silica gel desiccant is active. Clean the insulating glass surfaces and quartz suspension rod with anhydrous ethanol, and verify that the relative humidity inside the chamber reads below 25%.
Why this step matters
Water film condensation on insulating surfaces causes rapid electrostatic charge leakage by surface conduction, distorting force measurements.
Zero Balance and Torsion Wire Alignment
Adjust the leveling screws of the balance until the suspended dielectric beam swings freely without touching the chamber walls. Rotate the top torsion head dial until the index hair on the suspended sphere A aligns exactly with the chamber zero mark when both spheres are uncharged.
Why this step matters
Eliminating mechanical zero-offset torque ensures that any angular twist observed during measurement is purely caused by electrostatic Coulomb forces.
Regulated Sphere Charging and Charge Verification
Connect the charging probe to the 3.0 kV regulated DC supply. Touch the probe simultaneously to the suspended sphere A and sliding sphere B while they are in contact, depositing an equal charge of q1 = q2 = 20.0 nC on both spheres. Verify the charge magnitude with the Faraday ice pail and electrometer.
Why this step matters
Simultaneous contact charging of identical conducting spheres ensures strictly equal charge distribution (q1 = q2) by capacitive symmetry.
Coulomb Force Measurement vs Separation Distance
Advance the sliding carrier to position sphere B at a center-to-center separation distance of r = 4.0 cm from sphere A. As electrostatic repulsion deflects sphere A, rotate the torsion head dial until sphere A is restored precisely to its original zero mark. Record the restoring angle theta and calculate the electrostatic force F in micro-newtons.
Why this step matters
The null-deflection restoration method maintains constant geometric orientation and lever arm length b, ensuring that the restoring torque kappa * theta is directly proportional to the Coulomb force F.
Systematic Separation Variation
Repeat the torsion null measurement for six discrete separation distances (r = 4.0, 5.0, 6.0, 7.0, 8.0, and 9.0 cm). For each station, record the separation distance r, the inverse square 1/r^2, and the measured repulsive force F.
Why this step matters
Collecting data across a wide range of separations provides the necessary range of 1/r^2 to rigorously test the inverse-square law via linear regression.
Faraday Ice Pail and Charge Distribution Audit
Using the proof plane, sample the surface charge density from the sphere and transfer it into the Faraday ice pail to confirm zero interior charge and verify that total charge has not decayed significantly during the run.
Why this step matters
Monitoring charge retention throughout the experiment confirms that charge leakage remained negligible and that Gauss's law conditions were maintained.
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
F = k_e q_1 q_2 \left(\frac{1}{r^2}\right) \iff y = m x + b \iff k_e = \frac{m}{q^2}, \quad \varepsilon_0 = \frac{1}{4\pi k_e}
| # | Separation distance r (cm) | Electrostatic force F (μN) | Inverse square distance (1 / r²) | Electrostatic force F | Remove |
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No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING