1

COULOMB’S LAW LAB

CourseName

Coulomb’sLaw Lab

Abstract

This experimentwas conducted to determine the veracity of Coulomb’s Law. TheVirtual Physics Labs was used to conduct the experiment and collectthe vital data necessary to verify the law. The apparatus usedincluded a virtual charging rod, hanging pith balls, charging cat(cat fur), a protractor, ruler and grounding rod.

Some of the constants used in the calculations include (and which are gravitational constant and electrostatic constantrespectively. More experimental data was collected and recorder romthe information box at the Coulomb’s Law experiment.

Objectives

This lab soughtto demonstrate the veracity of Coulomb’s Law by observing differentequilibrium conditions of equally charged spheres. These spheres weresuspended as pendulums and the charge on the spheres (pith balls),their mass, and the electrostatic constant *k *were determined.

Procedure

Afterfamiliarization with the working of the Virtual Physics Labs, theexperimental setup, and the equipment provided, the experiment wasstarted. The pith balls are made very small in order to reduce theeffect of skewing outward and away from one another when charged andclose to one another. It was also assumed that the charge on eachpith ball adopted a spherical distribution in order to conform toCoulomb’s Law.

After startingup the “Coulomb’s Law” apparatus, the charging ball was chargedby rubbing the ball against the cat’s fur. This process wasrepeated until the charge number (#) read 120, indicating that theball was fully charged. The charge on the pith balls was then zero.Part of the excess charge on the charging ball was transferred ontothe neutral pith balls to charge them. the balls were then forcedapart by the Coulomb repulsion force between them. A protractor wasthen used to measure the angle of deflection (θ). A ruler was thenused to measure the distance *r* between the centers of the pithballs. These values were then recorded together with the value ofcharge given for each pith ball. This procedure was repeated for twomore values of charge number (# = 100 and # = 80) and resultsrecorded along with the Lab’s value of charge. The length of thependulum was also measured and recorded when # = 100 and the valuerecorded.

ExperimentalData

The mass of eachpith ball was given as = 0.05 grams. The table below details datathat was acquired from the virtual Coulomb’s Law experiment.

Charge Number # |
Variables |
Charge on each ball (C) |

120 |
Separation distance (r) = 17cm Separation angle (θ) = 35° |
6.168e |

100 |
Separation distance (r) = 14cm Length of the pendulum = 0.20m |
4.692e |

80 |
Separation distance (r) = 11cm Separation angle (θ) = 16° |
3.357e |

Table 1:Experimental data from the Virtual Coulomb’s Law Lab experiment.

Results

a. Calculatingthe charge on the pith balls

From Coulomb’sLaw, F = *k* . However, the forces acting on the pith balls are its weight, w, acting downwards, the string’s tension, T, and the electrostaticforce, F_{e}. The angle of separation is given as 35°. Thefollowing is the free body diagram of one of the balls.

Figure1: Free body diagram of one of the pith balls

Since the ball isin equilibrium, Newton’s law on equilibrium can be applied.

Σ *F**y*= 0, Σ *F**x *= 0

*T**y *−*w *= 0, *F*e − *T**x *= 0

*T *sin θ =*w*, *F*e = *T *cos θ

*F*e/w =*T *cos θ/ T sin θ = 1/tan θ

*F*e =*w*/tan θ

*kq*^{2}/r^{2}= *m*g/tan θ

Therefore, q = = = 3.321 x 10^{-8}C

b. Calculatingmass of the pith ball and tension on the string

Figure2: Free body diagram for one of the pith balls

F_{e} = *k*and q is given as 4.692 x 10^{-9}C. q^{2} = 2.201 x10 ^{-17} C^{2}

F_{e }=8.99 x 10^{9} N.m^{2}/C^{2} = 1.01×10^{-5 }N.

However, F_{e}= w/tan θ. Thus, w = F_{e} tan θ

θ = = = 69.5°

w = m x g = 1.01x 10^{-5}N xtan 69.5° = 2.701 x 10^{-5}N.

Mass of pith ball= 2.701 x 10^{-5}N/9.80m/s^{2} = 2.756 x 10^{-6 }kg

Tension on thestring is given by T sin θ = w. Therefore, T = w/sin θ

Therefore, T =2.701 x 10^{-5}N/sin69.5°= 2.884 x 10^{-5}N

c. Calculatingthe electrostatic constant, k

Figure3: Free body diagram for one of the pith balls

F_{e} = *k*. Thus k = since charge q is assumed to be equally distributed on eachball.

F_{e} =w/tan θ and θ = = = 74°

F_{e} =(5 x 10^{-5}x 9.8m/s^{2})/tan 74° = 1. 405 x 10^{-4}N

Thus, k = 9.907 N.m^{2}/C^{2}

Discussionand Analysis

The calculatedvalue of charge was 3.321 x 10^{-8}C while the expected value was 6.168e-9 C (7.611 x10 ^{-4}C). Percentage error can be calculated as follows:

(3.321 x 10^{-8}C x 100)/ 7.611 x10 ^{-4 }C = 4.36 x 10^{-3}%. The number of electrons residing on each pith ball can bedetermined using the relationship, Q = n . e where n is the number ofelectrons and e is the electron charge (1.6 x 10^{-19}C).

Therefore, n =3.321 x 10^{-8}C/1.6 x 10^{-19}C = 2.076 x 10^{11}.

,while

F_{grav }== 5.765 x 10^{-5}N

F_{electro }=8.99 x 10^{9}Nm^{2}/C^{2}^{= }3.343 x 10^{-4}N

Therefore,F_{electro}/ F_{grav} = 3.343 x 10^{-4}N/5.765x 10^{-5}N = 5.799

For the thirdpart, the percentage error can be calculated as follows:

Percentage error^{}= (9.907 N.m^{2}/C^{2}x 100%)/8.99 x 10^{9}N.m^{2}/C^{2 }= 1.102 x 10^{-7 }%

Newton’s Law ofequilibrium was used to determine various variables required above.

Conclusion

Coulomb’s Lawshows the relationship between the force between two point chargesand the charges and distance separating them. Coupled with Newton’slaw on equilibrium, various variables such as the charge of the pithballs, their mass, and the electrostatic constant, could bedetermined from the free body diagrams. The objectives of thisexperiment were thus met.