Cavendish Spheres; 5B30.20

Location:

• Cabinet: Electrostatics (ES)

• Bay: {[:ElectrostaticsCabinetB1B2: B1]}

• Shelf: #1

attachment:CavendishSpheres_5B3020.jpg

Description:

Cavendish used an apparatus consisting of two concentric spheres in 1772, insulated from each other and from ground, to prove the inverse square law of electrostatic force. This elegant experiment requires some investment of time by the demonstrator beforehand, to track down extraneous effects that could dominate the desired effect.

Setup:

1. Connect the Faraday cage to the Kethly Electrometer, ground on the outside of cage. Make sure the leads are twisted around each other to help cancel external charges. The Kethly Electrometer will be much more sensitive to charging due to the wires rubbing against each other if they are allowed to move.
2. Connect a short lead (red wire in picture) to the outside cage, to used as a (momentarily) ground for the inside cage, if in the event it accidentally gets charged or you can't remove the charge by touching both meshes with your fingers.
3. Set the Kethly Electrometer to 30V full-range and to measure 0V at half-range.
4. Remove the top hemisphere.
5. Connect the outer hemisphere to the outside of the cage (ie. blue wire shown in picture).
6. Connect the positive terminal of the Pasco 1000V DC Power Supply to the inner sphere (ie. yellow wire shown in picture).

7. Do not connect the ground terminal of the Pasco 1000V DC Power Supply to anything. The Power supply and Electrometer share a common ground through the power cord.

8. Raise the inner sphere to a potential of 1000V.
9. Ground the proof plane, the proof plane handle, and your fingers by touching each of them to the outside cage.

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

1. Touch the proof plane to the inner sphere
2. Bring the proof plane inside the inside cage. Electrometer needle should deflect positive by about 6V. This indicates there is positive charge on the inner sphere
3. Ground the proof plane on the outside cage. Touch the proof plane to the outside of the bottom hemisphere. Bring the proof plane inside the inside cage. Needle should not deflect. This indicates there is no charge on the outside of the bottom hemisphere.
4. Ground the proof plane on the outside cage. Touch the proof plane to the inside of the bottom hemisphere. Bring the proof plane inside the inside cage. Needle should deflect negative almost 6V. This indicates there is negative charge on the inside of the outer hemisphere.
5. Disconnect the yellow wire from the inner sphere connector. Turn off the power supply.
6. 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.

Demonstration:

1. Replace the outer upper hemisphere.
2. 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.
3. Replace the grounding wire (the blue lead) on the outside cage. This grounds the outer sphere.
4. Remove the outer top hemisphere.
5. 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.

Cautions, Warnings, or Safety Concerns:

1. This demonstration requires practice
2. Setup time is at least 10 minutes
3. No not wear wool or a sweater

References:

1. [http://books.google.com/books?id=4wZVAAAAMAAJ&pg=PA111&lpg=PA111&dq=Cavendish+Concentric+spheres&source=bl&ots=jjPTyWVN8Q&sig=1ZVTJc6D9NI3h7fRw1SGeEhgkzk&hl=en&ei=3bydSaqHGoT6MsHthM8L&sa=X&oi=book_result&resnum=7&ct=result#PPR3,M1 "The Electrical Researches of the Honourable Henry Cavendish", edited by James Clerk Maxwell], pages 104-113. UW-Copy

2. [http://books.google.com/books?id=3gYJAAAAIAAJ&pg=PR24&dq=cavendish+henry#PPA104,M1 "The Electrical Researches of the Honourable Henry Cavendish", edited by James Clerk Maxwell, Cambridge: University Press (1879)] Pages 104-113

3. "Classical Electrodynamics", 2nd Edition J.D.Jackson, Pages 5-7

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