SCHOOL NAME SCHOOL NAME SCHOOL NAME...has carried out his work for the investigatory project entitled _____ ... A categorized blogging website and an Online Resource Centre For CBSE,

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www.ammhu.com A categorized blogging website and an Online Resource Centre For CBSE, RBSE, and Other State Boards — Raj Kumar Parashari, Head Science @ JPHS, Jaipur-302021

SCHOOL NAME SCHOOL NAME SCHOOL NAME

ADDRESS WITH PINCODE AND PHONE NUMBER

Submitted by Guided by

Student Name [ Teacher Name ]

XII Sc ……

Board Roll No. Designation

-----------

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INDEX

1. CERTIFICATE

2. ACKNOWLEDGEMENT

3. AIM

4. APPARATUS REQUIRED

5. PRINCIPLE / THEORY

6. EXPERIMENTAL SETUP & PROCEDURE

8. OBSERVATIONS

9. CALCULATIONS

10. RESULT

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CERTIFICATE

This is to certify that _______________________

student of ______ school name _______, class XII Sc __

has carried out his work for the investigatory project

entitled _______________________________________

under my guidance and supervision.

Signature of the Teacher

Name Of The Teacher

Designation

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ACKNOWLEDGEMENT I __________________________________ a student of

____________________________________,______________

would like to pay my sincere gratitude to my Physics teacher

Mr./Mrs. __________________________ for helping and

guiding me throughout the completion of the project report. I

would like to thank Mr./Mrs. _______________________ our

school principal/Director for making school such a wonderful

place of learning. I also would like to thank Mr.

______________ our lab assistant for the timely assistant in

completion of the project.

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AIM To produce & verify cylindrical equipotential surfaces.

APPARATUS REQUIRED A battery eliminator, aluminum foil, a cylindrical container,

an optical bench needle, water and a multi-meter.

THEORY

1. Equipotential Surfaces It is a surface whose every point has same electric

potential. The equipotential surface may be surface can be

both real as in case of a charged conductor or an imaginary

as in case of a point charge or a dipole. Following are a few

examples of equipotential surfaces.

(a) Due to isolated point charges (b) Due to an electric dipole

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(c) Due to like charges (d) Due to a Sheet of Charge

2.Important Properties of Equipotential Surfaces.

(a). Work done in moving a test charge over an

equipotential surface is zero.

Let A an B be two points over an equipotential

surface, as shown in figure. If the test charge 0q is moved

from A to B, the work done will be

ABW Charge × potential difference

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AB VVq 0

As the surface is equipotential, so 0 AB VV . Hence 0ABW .

(b). Electric field is always normal to the equipotential

surface at every point. If the field were not normal to the

equipotential surface, it would have a non-zero component

along the surface and it should move the charges on the

surface. But it is not the case as charges on the surface are

static. There is one more argument, if tangential force will

push charges along surface, so will do work and hence there

should be potential difference. Which is contrary to the

observed fact (i.e. no potential difference between any two

points on an equipotential surface and consequently no work

is required to move a test charge on the surface). Hence the

electric field must be normal to the equipotential surface at

every point.

(c). Equipotential surfaces are closer together in the

regions of strong field and farther apart in the regions of

weak field. We know that electric field at any point is equal

to the negative of potential gradient at that point.

i.e., V

Er

or V

rE

For the same change in the value of V i.e., when V =

constant , we have

1

rE

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Thus the spacing between the equipotential surfaces

will be smaller in the regions, where the electric field is

stronger and vice versa.

(d). Normal drawn to an equipotential surface gives

direction of electric field at that point. If they intersect, there

will be two directions of electric field at the point of

intersection which is not possible. Also there will be two

values of potential at the point of intersection, which is not

permitted.

(e) Using Gauss theorem, the electric field at distance r

E =c

r ……… (1)

So potential difference

∆𝑽 = − 𝒄

𝒓

𝒓

𝑹 𝒅𝒓 = −𝒄 𝐥𝐨𝐠𝒆 𝒓 𝑹

𝒓 = 𝒄 𝐥𝐨𝐠𝒆𝑹

𝒓

Or, V = V1 +c logeR – c loger

Or, V = a – c loger ……… (2)

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3. Experimental Setup & Procedure Following is the experimental setup.

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(a) Wrap aluminum foil all around the curved wall of the

cylindrical container as shown above.

(b) Place an optical bench needle in the middle and apply

potential difference between the two using the battery

eliminator.

(c) Use a multi-meter to measure potential of any point

within water taking with respect to periphery as the lower

potential surface.

OBSERVATIONS:—

S.No. Radius Of The Cylinder

Height Electric potential with respect to needle VA

volt) VB(volt) VC(volt) VD(volt)

1 cm 2.42 2.38 2.41 2.42

1. r= 4 cm 2 cm 2.41 2.36 2.41 2.45

3 cm 2.41 2.38 2.44 2.44

1 cm 1.63 1.62 1.62 1.66

2. r= 6cm 2 cm 1.62 1.66 1.66 1.62

3 cm 1.61 1.65 1.64 1.64

3.

r = 8 cm

1cm 0.72 0.72 0.76 0.72

2 cm 0.72 0.74 0.72 0.72

3 cm 0.72 0.74 0.72 0.75

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Result-

(1) Equipotential surfaces are nearly coaxial.

(2) Difference in potential decreases more

rapidly as radius increases, which clearly

suggests that as we move radially outwards,

separation between the two equipotential

surfaces should increase.

(3) Electric potential decreases linearly loge(r),

which has been clearly verified by the V vs

loger graph.

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Precautions: —(a) All the connection should be

tight.

(b) Aluminum foil should be wrapped on the

walls of the container carefully.

(c) Data may be insufficient for accurate

inference.

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Bibliography

1. Video Lecture on Electrostatics by H.C. Verma on

www.youtube.com

2. NCERT

3. Fundamentals Of Physics Halliday & Resnick

Note: — Hand written Investigatory Project Report

should be submitted. Work should be neat and clean.

Avoid unnecessary fancy decoration of the project

report.

Note: — Learn theory, working and related viva for

board practical examination.

Wish you all the best.

Raj Kumar Parashari

Head Science

JPHS, Jaipur-21

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SCHOOL NAME SCHOOL NAME SCHOOL NAME...has carried out his work for the investigatory project entitled _____ ... A categorized blogging website and an Online Resource Centre For CBSE,