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Coulomb's law experiment Determination of Electric Constant

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### Coulomb's law experiment Determination of Electric Constant

By David Khutsishvili

Supervisor: TeimurazChichua

Email: [email protected]

Georgian Technical University Physics Department

Coulomb's Law Apparatus

A dielectric sphere covered with thin-layered silver conductor.

Thin inflexible rod.

The rotating cylinder hub (The RMS (B)).

A counterbalance.

Thin elastic thread made of hardened steel.

The Rotary Motion Sensor (A).

Rotating handle.

Clip.

Georgian Technical University Physics Department

9. Cylinder blocks.

Arresting Fixator.

Silver coated dielectric sphere (same as 1).

Caliper.

Degree scale.

Georgian Technical University Physics Department

Theory

The action of the small weights produces twist moment M1 of the thread. The result of twisting thread with α1 angle produces balancing moment of a spin moment, which within the limits of elastic-deformation strength, is proportional to the twisting α1 angle:

- The electrostatic interaction force between two spheres also causes the rise of the twisting M2moment of the thread with α2 angle:

Georgian Technical University Physics Department

Twisting α1 and α2 angles can be determined with turning a handle of the rotary motion B sensor.

According to Coulomb’s law, for vacuum (air):

Where:

r is the distance between two spheres centers, which is determined by that is on the Fig.3 is illustrated considering the geometrical correlation.

Using (1) and (2) formulas we get a complicated formula of electric constant:

Georgian Technical University Physics Department

With his experiments Coulomb found the calculation simplification method. This method, using in this presented torsion balance construction, is carried out as follows: The rotary motion B sensor is used for torsion calibration: With small weights action, produces the twisting moment of the thread, turned yoke to α1 angle, turning the upper handle (7) should get back the yoke to the starting position. This time the thread twisting reduces an angle from α1 to zero, however the upper part of the thread twists the opposite direction of α1 angle. It turns to γ1 angle, bigger than α1, which causes the twisting moment of the upper part of the thread:

Similar to all above, when we charge spheres equal and single charges, the yoke will turn effected by the electrostatic interaction between two spheres. It will turn to α2 angle; let’s begin turning 7 handle that produces elastic force’s balancing moment which returns the spheres to beginning r0distance between them. We measureγ1and γ2angles using rotary motion sensor (A )on the upper part of the stand.

In this case, balancing condition of charged spheres would be:

Georgian Technical University Physics Department

When we equalize η from (4) and (5) equations we get:

From this equation we get simpler formula of the electric constant:

Georgian Technical University Physics Department

Equipment

Georgian Technical University Physics Department

Thank you for the attention

Georgian Technical University Physics Department

Source:www.pasco.comwww.elearning.gtu.gehttp://mechatronics.mech.northwestern.edu/design_ref/sensors/encoders.htmlhttp://en.wikipedia.org/wiki/Eddy_current

Georgian Technical University Physics Department

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