Class XII Electroststics Electric Potential Energy

1. PPT 4 - ELECTROSTATIC
POTENTIAL ENERGY

2. ELECTRIC POTENTIAL ENERGY OF A CHARGE AT A POINT
• It is the minimum work done by an external force to bring a charge “q” from
infinity to that point without acceleration in electric field.
• Electric potential energy is the energy that is needed to move a charge against an
electric field.
• We need more energy to move a charge further in the electric field, but also
more energy to move it through a stronger electric field.
• It is denoted by “U”.
W∞B = UB - U∞ = UB

3. ELECTROSTATIC POTENTIAL OF A POINT
• The electric potential (also called the electric field potential, electrostatic potential) is defined
as the amount of work energy needed to move a unit positive test charge from a reference
point to the specific point in an electric field.
• It is denoted by “V”
• VB = W∞B / q
• Its SI unit is Volt (J/c)

4. CONSERVATION OF ELECTROSTATIC FORCE
The work done by Electrostatic force on a particle depends only on the initial and
final position of the particle, and not on the path followed. This can be proved by
showing the net work done on a charge by electric field in a closed path is zero.
Mathematically it is written as:

5. ELECTROSTATIC POTENTIAL DUE TO A POINT CHARGE

6. Variation of Electric field Intensity (E) and Electric Potential (V)
with distance (r)

7. ELECTROSTATIC POTENTIAL DUE TO GROUP OF CHARGE

8. ELECTROSTATIC POTENTIAL AT A POINT DUE TO ELECTRIC DIPOLE

9. EQUIPOTENTIAL SURFACE
• The locus of all points at the same potential is known as the
equipotential surface.
• No work is required to move a charge from one point to another
on the equipotential surface.
• In other words, any surface with the same electric potential at
every point is termed as an equipotential surface.

10. PROPERTIES OF EQUIPOTENTIAL SURFACE
1. The electric field is always perpendicular to an equipotential surface. It is because if the field is not
perpendicular to surface than there will be some component of electric field acting along the surface
and hence the work done in moving the charge in an equipotential surface will not be zero.
2. Two equipotential surfaces can never intersect. It is because different equipotential surfaces have
different potential, if they are intersecting it means that at the point of intersection both surfaces has
same potential which is not possible.
3. For a point charge, the equipotential surfaces are concentric spherical shells.
4. The direction of the equipotential surface is from high potential to low potential.
5. In a uniform electric field, any plane normal to the field direction is an equipotential surface.

11. PROPERTIES OF EQUIPOTENTIAL SURFACE
6. Inside a hollow charged spherical conductor , the potential is constant. This can be treated as
equipotential volume. No work is required to move a charge from the center to the surface.
7. For an isolated point charge, the equipotential surface is a sphere. i.e. concentric spheres
around the point charge are different equipotential surfaces.
8. The spacing between equipotential surfaces enables us to identify regions of a strong and
weak field i.e. E= −dV/dr ⇒ E ∝ 1/dr

12. RELATION BETWEEN ELECTRIC FIELD AND
ELECTRIC POTENTIAL
The electric field exists if and only if there is an electric potential difference. If the charge is
uniform at all points, however high the electric potential is, there will not be any electric field.
Thus, the relation between electric field and electric potential can be generally expressed as –
“Electric field is the negative space derivative of electric potential.”
i.e. E= −dV/dr

14. ELECTROSTATIC P.E. OF SYSTEM OF CHARGE
The electric potential energy of any given charge or system of changes is termed as
the total work done by an external agent in bringing the charge or the system of
charges from infinity to the present configuration without undergoing any
acceleration.

16. ELECTRIC FLUX
Electric flux, property of an electric field that may be thought of as the number of
electric lines of force (or electric field lines) that intersect a given area. Electric field
lines are considered to originate on positive electric charges and to terminate on
negative charges.
The International System of Units(SI) the net flux of an electric field through any
closed surface is equal to the enclosed charge, in units of coulombs, divided by a
constant, called the permittivity of free space; in the centi metre-gram-second
system the net flux of an electric field through any closed surface is equal to the
constant 4π times the enclosed charge, in electrostatic units (esu).

17. GAUSS LAW
According to the Gauss law, the total flux linked with a closed surface is
1/ε0 times the charge enclosed by the closed surface.
For example, a point charge q is placed inside a cube of edge ‘a’. Now,
as per Gauss law, the flux through each face of the cube is q/6ε0.

18. PROOF OF GAUSS LAW

20. DEDUCTION OF COULOMB LAW FROM GAUSS LAW
To deduce coulomb’s law from Gauss theorem: Consider that two point charge q1
and q2 are placed at point A and B at a distance r apart in vacuum. Let E is
magnitude of electric field at the location of point charge q2 due to charge
q2 Then force experienced by the point charge q2 due to electric field of charge
q1.

22. APPLICATION OF GAUSS LAW
Consider an infinitely long straight wire carrying a uniformly distributed positive charge. Its linear charge density, 𝜆,
is the charge per unit length of the wire, i.e., 𝜆 = q/l, where q is the total charge on the conductor distributed over
length l of the wire. The wire considered has an axis of symmetry. In order to calculate the electric field strength due
to the wire, let us consider a Gaussian cylinder of radius r and length l around the wire.
Using Gauss' Law, the electric field strength due to an infinite long straight wire is expressed as
Where r is the distance of a point under consideration and 𝜆 is the linear charge density of the wire.

23. ELECTRIC FIELD INTENSITY DUE TO UNIFORMLY CHARGES

25. FIELD DUE TO THIN INFINITE PLANE SHEET OF CHARGES

26. SPHERICAL SHELL
1) Electric field due to non conducting solid sphere.

27. 2) Electric field intensity due to two thin infinite parallel sheet