This presentation is about electric potential. As we know, electric fields are vector quantities, which define electric field properties. The electric properties of space can also be described by electric potential. Electric potential is scaler. The concept of electric potential is more important due to its advantages over electric field as it has no direction which make it simpler. Electric potential is more practical than the electric field because differences in potential. Electric potentials and electric fields are associated with each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy is meaningful only in terms of the difference in potential energy in respect of reference point. The most important fact is that the Electric potential have similar characteristics as that of gravitational potential energy.

1. Electric
Potential

2. It is the degree of electrification of a
body
It determines the direction of flowof charge
between twoelectrified bodies when placed in
contact.
The charge flows froma body at higher potential to a
body having lower potential. The flowremains
continue till both potential become equal.
Physical Significance of Electric Potential:
Electric Potential:

3. It is an important concept in studying
electrical circuitswhere the direction of flow
of electric charges is the core part of study.
Electric Potential Energy:
It is the amount of work required tomove a
unit charge frominfinity toa point inside the
field without producing an acceleration.
Concept of Electric Potential:

4. It is a point used todescribe the position of
any object.
It is a "zero point" where the potential energy is zero.
Concept of Reference Point in Electric
potential “zero Potential”:
In electric Potential, the reference point is the
Earth or a point at infinity, although any point can
be used.
Reference Point:

5. Expression:
Statement: It is the amount of work done by
a source charge tomove a unit charge from
infinity toa point inside the field without
producing an acceleration.
Let us consider a unit test charge,
brought frominfinity toa point ‘B’
Doing that amount of work done by
source charge.
Over small displacement ‘dr’ i.e., AtoB
= − θ
Electric Potential Energy

6. = − 0 θ
= − 0 .
= − 0 .
= 0
⃗. = cos θ
This amount of work done store in the formof PE(U)
− = − 0 .
= − 0 .
= 0; ∞

7. 1. Charge should be very-2 small, so it
can not disturbed electric field of
source charge
2. The motion of charge should be
uniform, so no acceleration produce
on test charge ‘ 0’
3. Charge ‘ 0’ should placed at infinity
4. Work is done by source charge ‘ ’
Important Points:

8. Statement:
It is the amount of work done by a
source charge tomove a unit charge
frominfinity toa point inside the field
without producing an acceleration.
=
q0
Electric Potential at any Point:

9. Statement:
It is the amount of work done by a
source charge tomove a unit charge
fromone point toanother point inside
the field without producing an
acceleration.
- =
q0
>
Electrostatic Potential Difference

10. Unit:
=
q0
volt (V) or JC-1
Define 1 volt:
If one joul work is done in moving the
positive charge of one coulomb fromone
point toanother point inside the field.
Then that potential is said tobe 1 volt
Dimensional Formula:
[M L2 T-3 A-1]
=
[M L2 T−2]
[AT]
Electrostatic Potential Difference

11. Let ‘ 0‘ be test charge brought frominfinity
to point ‘B’. Let ‘ ’ & ‘ ’ potential at A& B,
respectively. Then according to statement:
= θ
= 180°
= −
- =
q0
…. (1)
>
180° = -1
Electric Potential Due to a
Point Charge:

12. = −
4π 0
1
=
1
4π 0
= −
1
4π 0
= −
4π 0
=
+ 1
+ 1
− 1
−1
= −
4π 0
− 1
−1
=

13. 1
=
=
4π 0
1
=
4π 0
1
−
1
∞
=
4π 0
1 ∞ = 0
= 0
ℎ ℎ

14. Variation of ‘V’ with ‘r’

15. Let ‘ 0‘ be test charge brought
frominfinity to their
respective positions one by
one i.e., 1, 2, 3,
and so on,
respectively.
= 1 + 2 + 3 + ………. (1)
Electric Potential Due to a
Group of Point Charges:
Total Potential due to all charges at point P:
Consider a systemcontaining number of
charges i.e., 1, 2, 3,
and soon.

16. = θ
= 180°
= −
>
180° = -1
NowPotential due to 1 :
- =
q0
….. (2)
=
1
4π 0
1
= −
1
4π 0
1

17. = −
1
4π 0
1
= −
1
4π 0
=
+ 1
−1= −
1
4π 0 −1
=
=
1
4π 0
1

18. 2
1 =
=
1
4π 0
1
1
−
1
∞
=
1
4π 0
1
1
∞ = 0
= 0
= 1
Similarlly, potential due 2 :
2 = ;

19. = + + …….
1
=
1
4π 0
= [ + + …….. + ]
ℎ ℎ
due to a group
of charges

20. Prove :
q0
= ⋅
Let a charge allowed tomove fromAto B.
Then work done over small displacement ‘dl’:
= − θ … … (1)
= ⨯
= −q0 θ
W =−q0 ⋅
q0
= − ⋅ ….. (2)
Which we have toprove

21. Prove : Work done/unit test charge
independent of Path Followed
Since we knowthat:
q0
= − ⋅
. Δ
θ =
⇒ θ =
q0
= − ∫ θ ….. (1)

22. 1
q0
= − ∫
=
1
4π 0
= −
= − ∫
= −
4π 0 −1
q0
= − ……. (2)
Which we have to
prove

23. Prove : Work done/unit test charge
over close Path is zero
Part I: Ato B, Since we knowthat:
q0
= − ⋅
. Δ
θ =
⇒ θ =
q0
= − ∫ θ ….. (1)

24. 1
q0
= − ∫
=
1
4π 0
= −
= − ∫
= −
4π 0 −1
q0
= − ……. (2)

25. Part II: similarly Bto A:
q0
= − ……. (3)
Now:
q0
=
q0
+
q0
Using; (2)& (3)
q0
= 0 Which we have to
prove

26. Prove : Line Integral of Electric
Field over close Path is zero
Part I: Ato B, Since we knowthat:
⋅ = ∫ θ … … . (1)
. Δ
θ =
⇒ θ =
⋅ = ∫1) ⇒

27. = ∫
=
1
4π 0
=
= ∫
=
4π 0 −1
⋅ = − − ……. (2)

28. Part II: similarly Bto A:
Now:
Which we have toprove
⋅ = ⋅ + ⋅
⋅ = − − ……. (3)
⋅ = 0 Using; (2)& (3)

29. Expression for Potential Gradient
Since we knowthat:
( + ) - =
q0
=
q0
….. (1)
= θ
= q0 180°
= −q0
180° = − 1

30. = −q0
(1) implies
= −
= −
Which is required expression for
Potential Gradient

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