This document is a physics investigatory project certificate that certifies a student's successful completion of a project estimating the charge induced on two identical styrofoam or pith balls using Coulomb's law. It outlines the historical context of electricity and magnetism, the aim and theory behind the experiment, the apparatus used, and detailed procedures for estimating the charge. The conclusion emphasizes the need for careful measurements and handling during the experiment.

1. 6/6/2016
name |SEC-‘’, ROLL NO.-
2016-17
CLASS-XII
PHYSICSINVESTIGATORY PROJECT

2. CERTIFICATE
This is to certify that _____________ of Class- XII , section- D
has successfully completed the physics investigatory project
entitled ,
“To estimate the charge induced on each one of the two identical
styro foam balls or pith balls suspended in a vertical plane by
making use of Coulomb’s law.”
This report is the result of her endeavours and
research. It is finalized under our guidance and supervision in the
academic year 2016-2017.
[MRS. SARASWATI SANKARAN] [MRS. ANURADHARAKSHIT]
Vice Principal ,PGT physics Principal
Department of physics DelhiPublic School,Kalinga
Delhi PublicSchool, Kalinga

4. ACKNOWLEDGEMENT
Intheaccomplishmentofthisprojectsuccessfully
manypeoplehavebestowedonmetheirblessings and
theirimmense support.
Iwouldliketoexpress myspecialthanksofgratitude
tomy teacherMrs. Saraswati Sankaran aswellasour
principalMrs. Anuradha Rakshit whogavemethe
goldenopportunitytodothiswonderfulprojecton
thetopic“Toestimatethechargeinducedoneachone
ofthetwoidenticalstyrofoamballsorpithballs
suspendedinaverticalplanebymakinguseof
Coulomb’slaw.”whichalsohelpedmeindoingalotof
research andIcame toknowaboutsomanynew
things.SecondlyI wouldalsolike tothankmyparents

5. andmy friendswhohelpedmealot infinalizingthis
projectwithinthegiventime.
Last butnottheleast Iwouldliketothankallthe
peoplewhohadhelpedmedirectlyorindirectlyduring
thecompletionof thisproject.
name
CLASS-XII

6. To estimate the
charge induced on
each one of the two
identical styro foam
balls or pith balls
suspended in a
vertical plane by
making use of
Coulomb’s law

7. INTRODUCTION
Ancient cultures around the Mediterranean knew that certain objects, such as rods of
amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus
made a series of observations on static electricity around 600 BC, from which he believed
that friction rendered amber magnetic, in contrast to minerals such as magnetite, which
needed no rubbing. Thales was incorrect in believing the attraction was due to a magnetic
effect, but later science would prove a link between magnetism and electricity. Electricity
would remain little more than an intellectual curiosity for millennia until 1600, when the
English scientist William Gilbert made a careful study of electricity and magnetism,
distinguishing the lodestone effect from static electricity produced by rubbing amber. He
coined the New Latin word electricus ("of amber" or "like amber", from ἤλεκτρον [elektron],
the Greek word for "amber") to refer to the property of attracting small objects after being
rubbed. This association gave rise to the English words "electric" and "electricity", which
made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646.
Early investigators of the 18th century who suspected that the electrical force diminished
with distance as the force of gravity did (i.e., as the inverse square of the distance) included
Daniel Bornoulli and Alessandro Volta, both of whom measured the force between plates of
a capacitor, and Franz Aeipinus who supposed the inverse-square law in 1758. Based on
experiments with electrically charged spheres, Joseph Priestly of England was among the
first to propose that electrical force followed an inverse square law, similar to Newton’s law
of universal gravitation. However, he did not generalize or elaborate on this. In 1767, he
conjectured that the force between charges varied as the inverse square of the distance.
In 1769, Scottish physicist John Robison announced that, according to his measurements, the
force of repulsion between two spheres with charges of the same sign varied as x−2.06. Inthe
early 1770s, the dependence of the force between charged bodies upon both distance and
charge had already been discovered, but not published, by Henry Cavendish of England.
Finally, in 1785, the French physicist Charles Augustin de Coulomb published his first three
reports of electricity and magnetism where he stated his law. This publication was essential to
the development of the theory of electromagnetism.He
used a torsion balance to study the repulsion and attraction
forces of charged particles, and determined that the
magnitude of the electric force between two point charges
is directly proportional to the product of the charges and
inversely proportional to the square of the distance
between them.The torsion balance consists of a bar
suspended from its middle by a thin fiber. The fiber acts as
a very weak torsion spring. In Coulomb's experiment, the
torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended
by a silk thread. The ball was charged with a known charge of static electricity, and a second
charged ball of the same polarity was brought near it. The two charged balls repelled one
another, twisting the fiber through a certain angle, which could be read from a scale on the
instrument. By knowing how much force it took to twist the fiber through a given angle,
Coulomb was able to calculate the force between the balls and derive his inverse-square
proportionality law.

8. AIM OF THE EXPERIMENT
To estimate the charge induced on each one of the
two identical styro foam balls or pith balls
suspended in a vertical plane by making use of
Coulomb’s law.
APPARATUS REQUIRED
Small size identical balls (pitch or soft plastic)
Physical balance or electrical balance
Half meter scale
Glass rod
Cotton thread
Silk cloth
Small stand

9. THEORY
The fundamental concept of electrostatics is electric charge. We are all familiar with the
fact that rubbing two materials together –for example, a rubber comb on cat fur-
produces a “static” charge. The process is called charging by friction. Surprisingly, the
exact physics of the process of charging by friction is poorly understood. However, it is
known that the making and breaking of contact between the two materials transfers the
charge.
The charged particles which make up the universe come in three kinds : positive,
negative and neutral. Neutral particles do not interact with electrical forces . Charged
particles exert electrical and magnetic forces on one another, but if the charges are
stationary ,the mutual force is very simple in form and is given by coulomb’s law
Where F is the electrical force between any two stationary charged particles with
charges q1 and q2(measured in coulombs), r is the separation distance between the
charges (measured in meters) , and k is a constant of nature (equal to
8.9875517873681764×109
N m2
C−2
or 9×109
N m2
C−2
inSI units)
The study of the Coulombforcesamongarrangementsof stationarychargedparticles iscalled
electrostatics.Coulomb’sLaw describesthree propertiesof the electrical force:
1. Force is inversely proportional to the square of the distance between the charges
and is directed along the straight line that connects their centers.
2. The forces is proportional to the products of the magnitude of the charges.
3. Two particles of the same charge exert a repulsive force on each other, and two
particles of opposite charge exert an attractive force on each other.

10. Most of the common objects we deal with in the macroscopic (human sized)
world are electrically neutral. They are composed of atoms of atom that consists
of negatively charged electrons moving in quantum motion around a positively
charged nucleus. The total negative charge of the electrons is equal to the total
positive charge . So the atoms as well as the entire object don’t have net electrical
charge. If we charge something by friction , there only occurs the transfer of
charges from one to another object.
A neutral particle is not affected by electrical forces. A charged object can attract
neutral object by the method of electrical polarization. For example, if a
negatively charged rod is brought close to an isolated neutral insulator, the
electrons in the atoms of the insulator will be pushed slightly away from the
negative rod, and the positive nuclei will be attracted slightly towards the
negative rod. There occurs induced polarization but net charge is always zero.
The polarization of charge in the insulator is small but now its positive charge is a little
closer to the negatively charged rod, and its negative charge is a bit far away. Thus the
positive charge is attracted to the rod more strongly than the negative charge is
repelled, and there is an overall net attraction.
If the negatively charged rod is brought near an isolated , neutral conductor , the
conductor will also be polarized. In the conductor , electrons are free to move through
the material , and some of them are repelled over to the opposite surface of the

11. conductor, leaving the surface near the negative rod with a net positive charge. The
conductor has been polarized and will now be attracted to the charged rod.
Now if we connect a conducting wire or any other conducting material from the
polarized conductor to the ground, we provide a “path” through which the electrons can
move. Electrons will actually move along this path to the ground. If the wire or path is
subsequently disconnected ,the conductor has been charged without actually being
touched with the charged rod. This process is called charging by induction.
Let the force between two stationary charges be F
F α q1q2
F α 1/r2
From the above two expressions,
F= k q1q2/r2
=1/4πε0 q1q2/r2
Where k = 9 x 109 Nm2/C2
And is called absolute permittivity of free space or vacuum =8.854 x 10-12
C2
/N/m2
Let the twoidentical pithballs (B1andB2) of mass‘m’ are hangedfromstringsof length‘l’each.
Whenthe two ballsare givencharge q1 and q2 respectivelythe electrostaticforce actingbetween
themwill be ,
F= k q1q2/r2
Because of this force, they are separated by a distance ‘r’ as shown in the figure .

12. Force acting on ball B1
(i)Weight of ball B1 , W= mg
(same as that of B2)
This can be resolvedin two components mgcos0 and
mgsin0 .
Component mgsin0 is the restoring component.
In state of equilibrium
Electrostatic force = mgsin0
Or , F = k q1q2/r2 = mgsin0
From OBC , sin0 =r/2l
k q1q2/r2 = mg r/2l
If both the identical pith balls have same
charge on them , then q1=q2=q
K q2 / r2 = mgr /2l
q= √mgr3/2kl
By putting the values of ‘m’ , ‘r’ , ‘l’, ‘g’ and ‘k’ we can estimate the charge on the two pith
identically chargedpith balls.

13. PROCEDURE
1.Measure the mass (m) of each of the two
identical pith balls using a physical balance.
2.Hang the two balls from a rigid support using
light silk or cotton threads of same length ‘l’.
3.Take a glass rod and rub it with a silk cloth to
induce charge on the rod. Now
touch the glass rod with both the
pith balls together so that equal
charge is induced on both the
balls.
4.When left freely, the two balls will repel each
other and when they are at rest separated away
from each other , measure the distance
between them.
5.To change the charge on ball, take third
uncharged ball touch it to any one of the two
balls and take the third ball away, again
measure the distance between the two hanging
balls.

14. OBSERVATIONS
Mass of the pith balls m= 01 gm.
Radius of the ball a= 0.1 cm.
Length of thread l= 9.5 cm.
Sl.no. Charge on Ball
B1
Charge on Ball
B2
Distance
between the two
balls (in cm)
01
02
03
04

15. CALCULATIONS
Charge on the pith ball q =
√mgr3
/2kl

16. CONCLUSION
The charge on pith balls
in different cases
are________ C.
1. The suspended balls should not
be touched by any conducting
body.
2. Rub the glass rod properly with
silk rod to produce more
charge.
3. Weight the mass of the balls
accurately.

17. BIBILOGRAPHY
Internet, Wikipedia , Google, NCERT physics book class-12