Experiment No:7, Verification of Coulomb’s law using Coulomb balance
Debdoot Ghosh, Roll No:-1811056
low.
ABSTRACT q1 q2
F “ Ke (1)
R2
In 1785, Coulomb developed his method for mea- where ke is the Coulomb constant. In SI units, the
suring the electric force between two charged ob- value of ke is 8.9875ˆ109 N m2 {C 2 . Coulomb’s force
jects. Coulomb created a torsion balance to do acts along the direct line of separation between the
this Experiment.The aims of this experiment is to two charges. Depending on the like or unlike na-
find relation between the Electrostatic force and ture of the point charges, the force is attractive
charge of charge particle or point charge and the or repulsive,respectively. In this experiment, we
distance between two point charge.And to eval- are going to verify the Coulomb’s law by using a
uate the coulomb’s constant.We have done this Coulomb balance.The inverse square behaviour with
experiment by torsion balance with two charged the charge separation distances appears almost ex-
sphere. We have plotted the graph between Θcorr act. One may write Coulomb force as, F 91{Rp2` q,
Vs R, Θcorr Vs 1{R2 , Θcorr Vs Q2 . But we get where is the deviation from the inverse square be-
some deviation from theoretical inverse square haviour.
force law due humidity in the air and for various
error source.We calculated the propagation error
Coulomb’s torsion balance:
and get the average value of coulomb’s constant
is: 5.091 ˆ 109 ` { ´ 0.55485 ˆ 109 N m2 C ´2 . The historical torsion balance designed by Coulomb
is shown in Fig 1. It comprised of a cylindrical glass
case and closed by a lid from which a glass tube
emerges out. The tube ends with a piece of metal
OBJECTIVE
from which a torsion fibre is suspended. This fibre
(I)To study Coulomb’s force as a function of the dis- holds a horizontal needle made of lac, with a brass
tance between two charges. disc at one end and a sphere at the other.The second
(II)To study Coulomb’s force as a function of charge. sphere is suspended through a hole on the lid of the
(III)To determine Coulomb’s constant. glass case. B is charged outside the case and placed
back touching the brass disc and thereby charging it
too. Due to the repulsion of two charged sphere the
fibre become twisted by certain angle. By knowing
THEORY
the angle, Coulomb was able to calculate the force
Electrostatic force between two charges is directly between the balls.
proportional to the magnitude of the product the
two charges and inversely proportional to the square Faraday’s ice pail:
of the distance between their centers. If q1 and q2
are the magnitude of the two point charges, and R British scientist Michael Faraday demonstrates the
is the distance between their centers, electrostatic effect of electrostatic induction on a conducting con-
force between them is expressed by the equation be- tainer. For a container, Faraday used a metal pail
made to hold ice, which gave the experiment its
0
name. The experiment shows that an electric charge
1
2
Coulomb force can be written as:
q1 q2
Fcorr “ B ¨ Ke 2 (3)
R
Torsion constant of the fibre:
When the torsion fibre is twisted by an angle , the
resulting torque is proportional to . As the torque
arm is constant here so torsion force is :
Ftor “ Ktor ¨ θ. Ktor is torsion constant.We can
calculate Ktor from the slope of the graph between
Ftor V sθ. At equilibrium Coulomb force F corr is
balanced by Ftor . Hence using Eqns (3) and (4), a
general working formula can be derived showing the
relation between the angle of twist, charge on the
spheres and the separation distance between them:
Ke q1 q2 θ
θcorr “ Ktor R2 . Where θcorr “ B.
Schematic diagram of the set up:
Figure 1: Coulomb’s torsion balance
enclosed inside a conducting shell induces an equal
charge on the shell, and that in an electrically con-
ducting body, the charge resides entirely on the sur-
face.It also demonstrates the principles behind elec-
tromagnetic shielding such as employed in the Fara-
day cage.The ice pail experiment was the first pre-
cise quantitative experiment on electrostatic charge.
Unit of charge:
The coulomb (symbol: C) is the International Sys-
tem of Units (SI) unit of electric charge. It is the
charge (symbol: Q or q) transported by a constant
current of one ampere in one second: 1C “ 1A ˆ 1s.
The charge on a single electron is 1.602 ˆ 10´ 19C. Figure 2: schematic diagram of set up
Corrections to the data
APPARATUS
As the charged sphere is not a point charge so we
(I)High Voltage Power Source (0- 6 kV),
see some amount of deviation from inverse square
(II)PASCO Coulomb Balance
force.when two charged spheres are separated by a
distance that is not large compared to the size of
the spheres, the charges will redistribute themselves
on the spheres so as to minimize the electrostatic OBSERVATION-1
energy.So the force between two charged sphere will Table-1
be less than two point charge at same distance. A
Table-1 Ktor “ 1.32 ˆ 10´6 N {˝ , C=149.05 pF ,
correction factor can be used to account for this de-
Supply voltage =6.10 V, Charge on each sphere =
viation. Using method of image charge, a first order
4471.5 ˆ 10´12 C
correction, B, can be calculated as
a3 OBSERVATION-2
B “1´4 (2)
R3
Table-2
where a equals the radius of the spheres and R is
the separation between spheres. Thus the corrected Table-2 R= 6 c.m.
3
Sl No: R(cm) Θ B Θcorr
1 20 8 0.999142625 8.00686488578145
2 19 9 0.999 9.00900900900901
3 18 11 0.99882390260631 11.0129523045022
4 17 13 0.998603907999186 13.0181745693815
5 16 16 0.998325439453125 16.026837910456
6 15 19 0.997967703703704 19.038692263774
7 14 24 0.997500364431487 24.0601415856911
8 13 29 0.996878015475649 29.0908210932538
9 12 34 0.996030671296296 34.1354950001191
10 11 39 0.994846731780616 39.202018516155
11 10 48 0.993141 48.3315057982703
12 9 53 0.99059122085048 53.5034016902516
13 8 61 0.986603515625 61.8282816085014
14 7 67 0.980002915451895 68.3671435498794
15 6 76 0.96824537037037 78.4925002749341
Table 1: Table of R Vs Θcorr for fixed V
Sl No. Supply Voltage (V) Voltage(V) Θ 1/2 Q Q Θcorr
1 2.05 12 7 1788.6 3577.2 7.23140495867769
2 3.02 22 26 3279.1 6558.2 26.8595041322314
3 4.02 32 35 4769.6 9539.2 36.1570247933884
4 4.45 39 39 5812.95 11625.9 40.2892561983471
5 3.8 29 31 4322.45 8644.9 32.0247933884297
6 5.08 46 49 6856.3 13712.6 50.6198347107438
7 5.86 51 66 7601.55 15203.1 68.1818181818182
8 6 56 74 8346.8 16693.6 76.4462809917355
Table 2: Table of V Vs Θcorr for fixed R
GRAPHS
Fig-3,Fig-4,Fig-5.
4
Figure 3: graph of Θcorr Vs R
Figure 4: graph of Θcorr Vs 1/R2
5
δQ “ 1.9567960629183 ˆ 10´16 C.
b
δC
C “ p2 δQ 2 δSlope 2
Q q ` p Slope q “ 0.055.
δC “ 0.055 ˆ 5.11 ˆ 109 “ 0.281 ˆ 109 N m2 C ´2 .
The error in Coulomb’s constant of Graph-3 is
δR “ 0.001m.
b
δC δSlope 2
C “ p2 δR 2
R q ` p Slope q “ 0.1634.
δC “ 0.1634 ˆ 5.072 ˆ 109 “ 0.8287N m2 C ´2
CONCLUSION
From this Experiment we get the relation between
Electrostatic Force with the amount of charge of the
spheres and with the distance between their center.
Figure 5: graph of Θcorr Vs Q2 But we get small deviation from inverse square force
law from the graph-1 and graph-2.
The coulomb’s constant found out from Graph-2
CALCULATION is:
5.11 ˆ 109 N m2 C ´2 ` { ´ 0.281 ˆ 109 N m2 C ´2 . The
From Graph-2
coulomb’s constant found out from Graph-3 is:
Slope of the graph is 5.072 ˆ 109 N m2 C ´2 ` { ´ 0.8287 ˆ 109 N m2 C ´2 .
m “ p3525.02 ` { ´ 194.6q ˆ 10´4 p˝ {m2 q. Average Value of Coulomb’s constant is:
5.091 ˆ 109 N m2 C ´2 ` { ´ 0.55485 ˆ 109 N m2 C ´2 .
The charge on the sphere is 17886 ˆ 10´12 C. We know the theoretical value of Coulomb’s con-
The Coulomb’s constant is: stant is:
C “ SlopeˆK
Q2
tor
8.99 ˆ 109 N m2 C ´2 . So we get less value than ac-
tual theoretical value because of the humidity in the
0.3525ˆ1.32ˆ10´ 6 atmosphere.Due to high humidity the spheres are
C“ p9543ˆ10´12 q2
discharged very quickly so it is very troublesome
C “ 5.11 ˆ 109 N m2 C ´2 . to take reading.And as the set up is very delicate
the result is affected by any close thing that acquire
charge.The main cause of this deviation is the leak-
From Graph-3 age of charge for various reason.
Slope of the graph is:
m “ 106740759.3 ` { ´ 17078521.49p˝ {C 2 q. REFERENCE
(I)Brooklyn College Lab Manual.
Distance between two spheres is 0.06 m. (II)University of Virginia Physics Department PHYS
636, Verifying Coulomb’s Law.
The Coulomb’s constant is: C “ Slope ˆ Ktor ˆ (III) Lab Manual.
R2 .
C “ 1.35 ˆ 10´6 ˆ 106740759.3 ˆ p0.06q2 .
C “ 5.072 ˆ 109 N m2 C ´2 .
ERROR ANALYSIS
The error in Coulomb’s constant of Graph-2 is
