Physics Home > Teaching Labs > Electricity & Magnetism > Electrostatic Balance

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#### Lab Activities

In this lab the students indirectly test the validity of Coulomb's Law.

The primary piece of apparatus consists of a parallel plate capacitor, the top plate of which is divided into two parts - a circular inner piece and an annular outer guard ring. The circular inner part of the upper plate is suspended from one arm of an equal arm balance. A similar plate is suspended from the other arm of the equal arm balance. Using a screw adjustment, the balance is adjusted so that at equilibrium the circular inner part of the upper plate of the capacitor is suspended just below the level of the plane of the annular ring. A mass placed on the plate on the other arm of the balance will disturb this balance and cause the circular plate of the capacitor to rise into the plane of the annular ring. Washers attached to the annular ring prevent the circular ring from rising above the plane of the ring and provide an electrical connection between the two parts.

When a voltage difference is applied between the plates, an attractive electrical force arises between the plates. The relationship between the voltage difference and this electrical force can be derived from Coulomb's law. It is

where x is the plate separation, e is the permittivity of a vacuum, A is the area of the circular plate, V is the potential difference between the plates and F is the electrostatic force. This electrical force can be used to restore the original balance. When the original balance is restored, the electrical force will equal the weight of the mass.

In the lab the students measure the voltages needed to bring the system back into its original balance for a variety of known masses. These voltages are then compared to the voltages predicted by the above formula. Experimental results tend to be within 8% of those predicted by theory. Capacitors with three different plate separations are available.

Other possible student activities include: (1) using the apparatus to calibrate a voltmeter in absolute units without the use of any electrical standards and (2) using the calibrated voltmeter to measure the open-circuit potential of a dry cell.

Introductory

#### Equipment

 Number of set-ups available:5 Per lab station: 1 large equal-arm balance 1 high voltage power supply (continuously variable) 1 digital voltmeter 1 switch box 1 vernier caliper 1 set of jeweler's screwdrivers 1 small level 1 pair of tweezers 1 set of masses containing: 2 100 mg masses 1 200 mg mass 1 500 mg mass 1 1000 mg mass 2 BNC cables 3 BNC to banana (male) adaptors 2 banana leads 1 parallell plate capacitor with annular ring 1 weight plate/string Per lab station: 1 800-1000 ml beaker 1 box of kimwhips 1 bottle of ethyl alcohol extra nylon washers for plate separation extra nylon screws

#### Notes

 Last Update: Site contact: largent@Dartmouth.EDU