Electromagnetism
Isolated conducting sphere
An isolated sphere of radius R has C = 4πε₀R — compare pF readout with textbook value.
Isolated conducting sphere — interactive Electromagnetism simulation. An isolated sphere of radius R has C = 4πε₀R — compare pF readout with textbook value. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Spherical capacitance
An isolated sphere of radius R has C = 4πε₀R — compare pF readout with textbook value.
An isolated conducting sphere of radius R at potential V stores charge Q = CV with C = 4πε₀R — capacitance grows linearly with radius. Charge sits on the outer surface; inside the conductor E = 0. Compare the pF readout with 4πε₀R for the displayed radius.
- C = 4πε₀R
- U = ½CV²
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A single isolated conducting sphere, charged to some voltage, has a capacitance too — even with no second plate nearby. If you raise the sphere's voltage, does the field just outside it rise in proportion?
Predictions to weigh
- No — the field depends on voltage in a more complex way.
- Yes — the exterior field is directly proportional to the sphere's voltage.
- The exterior field doesn't depend on the sphere's voltage at all.
Variable roles
What you set:
- Sphere voltage V (V)
What you measure:
- Capacitance C (pF)
- Exterior field E (N/C)
How the investigation runs
- Open the isolated-sphere preset and press Reset. The sphere's radius is fixed at 8 cm.
- Enable the exterior field-strength readout.
- Set the sphere's voltage for each trial and record the field strength measured at twice the sphere's radius from its center.
Governing equation
Isolated Sphere Capacitance — C = 4πε₀R
An isolated conducting sphere of radius R has capacitance C = 4πε₀R relative to infinity. Unlike a parallel-plate capacitor, it needs no second conductor nearby — 'the rest of space' acts as the other plate.
What the printable worksheet asks students to work out
- For one trial, compute C = 4πε₀R using R = 0.08 m (same in every trial), then E = V/(2R) for the field at radius 2R from center. Compare both to the table.
- Explain why, at a fixed measurement point (here, 2R from center), the exterior field scales linearly with the sphere's voltage — even though a point charge's field itself falls off as 1/r².
Where this shows up beyond the lab
- A Van de Graaff generator charges an isolated metal sphere to very high voltage. Its capacitance C = 4πε₀R is quite small for a lab-sized sphere, which is exactly why even a modest amount of charge can drive it to extremely high voltage (V = Q/C).
- The Earth itself behaves approximately like an isolated charged sphere with a small negative surface charge. Using C = 4πε₀R with Earth's radius (~6.4×10⁶ m), would you expect Earth's capacitance to be bigger or smaller than this experiment's 8 cm sphere?
- AP Physics 2 — Unit 10: Electric Force, Field, and Potential
- AP Physics C: Electricity and Magnetism — Unit 10: Conductors and Capacitors
- AP Physics C: Electricity and Magnetism — Unit 9: Electric Potential
- IB Physics — D.2 Electric and magnetic fields
- General High School Physics — Magnetism & electromagnetism
- NGSS High School Physics — Energy in particle motion and fields
- Welcome to Isolated Sphere
- Select the sphere
- Press Play
- Energy on a sphere
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.