Cavendish Spheres, 5B30.20

Location:

• Cabinet: Electricity & Magnetism Cabinets (E&M) (Right Side)

• Bay: (B1)

• Shelf: #1

Description:

In 1772 Cavendish used an apparatus consisting of two concentric spheres that are 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.

• RHS -- Means the Right-Hand-Side of the Electricity & Magnetism Cabinet Peninsula

Setup:

1. Connect the Faraday cage to the Keithley Electrometer by connecting the ground to the outside of cage and the positive lead to the inside. Make sure the two leads are twisted around each other to help cancel external charges. The Keithley Electrometer is sensitive to charging due to the wires rubbing against each other.
2. Connect a short lead (red wire in picture) to the outside cage. This wire can be used as a (momentary) grounding wire for the inside mesh in the event it accidentally gets charged or you can't remove the charge by touching both meshes with your fingers.
3. Set the Keithley Electrometer voltage range knob to 30V full-range and the scaling knob to 0V on center.
4. Remove the top hemisphere.
5. Connect the outer hemisphere to the outside of the cage (blue wire in photo).
6. Connect the positive terminal of the Pasco 1000V DC Power Supply to the inner sphere (yellow wire in photo).

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. How to ground the Proof Plane!
   • The Proof Plane and handle must be grounded
   • Best way to do this is with a burner or open flame by moving the Proof Plate through the open flame and then testing it in the Faraday Cage. Repeat if needed.
   • Another way is to simultaneously tough both meshes of the Faraday Cage with your fingers and touch or rub the Proof Plate to the inside of the Faraday Cage. Repeat if needed.

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 inner 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. The 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. The 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 inner cage. The needle should deflect almost as much as before.

Demonstration:

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 inner 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 inner cage. The 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 inner cage. The 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 inner cage. Needle should deflect almost as much as before.

Demonstration:

1. Replace the outer upper hemisphere.
2. Disconnect the grounding wire (blue wire in photo) 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 (blue wire in photo) 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. This was proposed by Cavendish as a consequence of the inverse square law of the electrostatic force. I.e. if the electrostatic force dropped off faster than inverse square, the inner and outer spheres would end up with charges of the same sign. Alternatively, 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. Do not wear wool or a sweater

References:

1. "The Electrical Researches of the Honourable Henry Cavendish", edited by James Clerk Maxwell, pages 104-113. UW-Copy

2. "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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