Cavendish Spheres 5B30.20

attachment:CavendishSpheres_5B3020.jpg

The Cavendish Spheres, Faraday Cage, and electrometer are located in [:ElectrostaticsCabinet:Electrostatics Cabinet], B1.

The 1000V DC Power Supply is located in [:ElectrostaticsCabinet:Electrostatics Cabinet], B2.

The proof plane is located in [:ElectrostaticsCabinet:Electrostatics Cabinet], A1.

Cavendish used this experiment to prove the inverse square law of electrostatic force.

Preliminaries:

• Connect the Faraday cage to the electrometer, grounding the outside cage.
• Set the electrometer to 30V full-range, and to measure 0V at half-range.
• Remove the outer top hemisphere.
• Connect the outer bottom hemisphere to the outside of the cage (blue wire in picture).
• Connect the positive 1000V terminal of the power supply to the inner sphere (yellow wire)
• Do not connect the ground terminal of the power supply to anything. Power supply and electrometer share a ground through the power cord.
• Raise the inner sphere to 1000V potential.
• Ground the proof plane, the proof plane handle, and your fingers by touching each of them to the outside cage

At this point the outer bottom hemisphere is grounded and the inner sphere is at 1000V. Make some measurements to gain confidence:

• Touch the proof plane to the inner sphere
• Bring the proof plane inside the inside cage. Electrometer needle should deflect positive by about 10V.
• Ground the proof plane on the outside cage. Touch the proof plane to the outer bottom hemisphere. Bring the proof plane inside the inside cage. Needle should not deflect.
• Disconnect the yellow wire from the inner sphere connector. Turn off the power supply.
• Ground the proof plane on the outside cage. Touch the proof plane to the inner sphere. Bring the proof plane inside the inside cage. Needle should deflect, almost as much as before.

Here is the actual Cavendish Experiment:

• Replace the outer upper hemisphere.
• Disconnect the grounding wire (ie the blue lead) from the outside cage, and touch it momentarily to the inner sphere connector. This brings the two spheres to the same potential.
• Replace the grounding wire (the blue lead) on the outside cage. This grounds the outer sphere.
• Remove the outer top hemisphere.
• Ground the proof plane on the outside cage. Touch the proof plane to the inner sphere. Bring the proof plane inside the inside cage. The needle should not deflect!

Discussion: The fact that the needle does not deflect on the last measurement shows that the inner sphere has been left neutral, and was proposed by Cavendish as a consequence of the inverse square law of the electrostatic force. If the electrostatic force dropped off faster than inverse square, the inner and outer spheres would end up with charges of the same sign. If the electrostatic force dropped off slower than inverse square, the inner and outer spheres would end up with charges of opposite sign. Only if the electrostatic force drops off as inverse square can the inner sphere end up with no charge.

Cavendish's account of his experiment may be found in "The Electrical Researches of Henry Cavendish", edited by James Clerk Maxwell, paragraphs 217-234.

Rub the black rod on the fur. The black rod charges negative, as can be demonstrated by bringing it inside the inside cage.

Touch the black rod to the lead to the inside sphere. The inside sphere is now charged negative, while the outside sphere remains neutral.

Briefly connect the inside sphere to the outside sphere.

The inside sphere is found to be uncharged, all of the charge having migrated to the outside sphere. The only power law for electrostatic force that allows this to happen is the inverse square law.

Note: this writeup is incomplete as of 5/30/08. No one at UW physics seems to have successfully used this demonstration.

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