6/6/2016

name |SEC-‘’, ROLL NO.-

2016-17 CLASS-XII PHYSICS INVESTIGATORY PROJECT

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. ANURADHA RAKSHIT]

Vice Principal ,PGT physics Principal

Department of physics Delhi Public School,Kalinga

Delhi Public School, Kalinga

ACKNOWLEDGEMENTIn the accomplishment of this project successfully many people have bestowed on me their blessings and their immense support. I would like to express my special thanks of gratitude to my teacher Mrs. Saraswati Sankaran as well as our principal Mrs. Anuradha Rakshit who gave me the golden opportunity to do this wonderful project on the topic “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.” which also helped me in doing a lot of research and I came to know about so many new things. Secondly I would also like to thank my parents and my friends who helped me a lot in finalizing this project within the given time.Last but not the least I would like to thank all the people who had helped me directly or

indirectly during the completion of this project. name

CLASS-XII

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

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. In the 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.

AIM OF THE EXPERIMENTTo 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 REQUIREDSmall size identical balls (pitch or soft plastic)Physical balance or electrical balanceHalf meter scale Glass rodCotton threadSilk clothSmall stand

THEORYThe 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 in SI units)

The study of the Coulomb forces among arrangements of stationary charged particles is called electrostatics. Coulomb’s Law describes three properties of 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.

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 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 two identical pith balls (B1 and B2) of mass ‘m’ are hanged from strings of length ‘l’ each .

When the two balls are given charge q1 and q2 respectively the electrostatic force acting between them will be ,

F= k q1q2/r2

Because of this force, they are separated by a distance ‘r’ as shown in the figure .

Force acting on ball B1

(i)Weight of ball B1 , W= mg

(same as that of B2)

This can be resolved in 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 charged pith balls.

PROCEDURE1. 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.

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)

01020304

CALCULATIONS

Charge on the pith ball q = √mgr3/2kl

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.

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