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To determine electrostatic force between two charged conducting spheres depends on the distance between the spheres and depends on the charge on the spheres.
Typology: Lab Reports
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Purpose
a. To determine how the electrostatic force between two charged conducting spheres depends on the distance between the spheres and b. To determine how the electrostatic force between two charged conducting spheres depends on the charge on the spheres.
Theory
Electrostatic force between two charges is (a) directly proportional to the magnitude of the product the two charges and (b) inversely proportional to the square of the distance between their centers.
If Q 1 and Q 2 are the magnitude of the two point charges, and R is the distance between their centers, electrostatic force between them is expressed by the equation below.
|𝑄 1 ||𝑄 2 | 𝑅^2
where k is a constant of proportionality, called Coulomb’s constant, k = 8.99 x 10^9 N.m^2 /C^2. In this experiment, you are going to verify the Coulomb’s law by using a Coulomb balance.
Apparatus
High Voltage Power Source (0- 6 kV), PASCO Coulomb Balance
Description of Apparatus
You will be using a Pasco Coulomb balance in this lab which is shown in Fig. 1. The Coulomb Balance is a delicate and very sensitive torsion balance that can be used to investigate the nature of the electrostatic force between charged objects. You will use two identical conductive spheres in this experiment. One conductive sphere is mounted on a rod which is counter- balanced and suspended on a thin torsion wire. An identical conductive sphere is mounted on a slide assembly so that it can be positioned at various distances from the suspended sphere. The spheres are held by plastic support rods for electrical insulation. The ruler on the slide assembly measures the distance between the centers of the two spheres when the suspended sphere is at its equilibrium position. When the conducting spheres are charged, the sphere suspended on torsion wire gets deflected due to electrostatic force. Rotating knob is used to bring the charged sphere back to equilibrium position.
Charged spheres
Torsion wire
Sliding assembly
Rotating Knob
Fig. 1. PASCO Coulomb balance
Complete experimental set up is shown in Fig. 2. The spheres are charged by means of a very stable high voltage (kilovolt) power supply and a charging probe. The electrostatic force between the spheres causes the torsion wire to twist. The torsion balance can be brought back to its equilibrium position by twisting the torsion wire in the opposite direction using the rotating knob. The angle through which the torsion wire must be twisted to reestablish equilibrium is directly proportional to the electrostatic force between the two spheres.
The proportionally constant depends on the torsional constant of the wire.
By varying the distance between the spheres and the amount of charge on the spheres, it is possible to verify Coulomb's Law. Although it is possible, using this apparatus, to measure the value of the constant, k, appearing in Coulomb's Law, we will not attempt to do so in the present experiment. We will attempt to verify that the value of the exponent of R is 2 and that the force is proportional to the product of the two charges.
Procedure
! CAUTION!
THE APPARATUS IS VERY DELICATE AND MUST BE HANDLED WITH CARE. Please pay close attention to using proper technique. Do not touch the spheres with your hands. Do not disturb the table where the Coulomb balance is sitting. If in doubt about any procedure, ask!
!!Be careful working in this lab since you are using a Kilovolt power supply!!
Fig. 2. Experimental set up
Charging probe (red)
High voltage power supply
Grounding probe (black)
Part II. Force versus Charge
In this part of the experiment, you will keep the distance between the spheres constant and measure the force for different values of the charge, keeping Q 1 = Q 2 always.
Computation and Analysis
Because you are using charged spheres rather than point charges to test Coulomb's Law, the effective distance between the charges is not equal to the distances between the centers of the spheres. An approximate expression for the corrected distance ( R’ ), adequate for our purposes, is given by
𝑅′ = 𝑅 (1 + 2.3 𝛽) (3)
with 𝛽 = 𝑎^3 𝑅^3 ^ and^ a^ = 1.90 cm
where R is the distance between the centers of the spheres and a is the radius of each sphere. It is assumed here that the conducting spheres are identical and carry identical charges.
For each value of R used in part I, calculate R' using the above expression. Also tabulate your
data for 1/(R')
2 , ln R' , and ln θ.
Question: Should this straight line pass through the origin? What can you conclude from this graph?
Questions to be answered in your report