1) The document discusses concepts related to work, energy, electric fields, and capacitors. It defines work, gravitational potential energy, kinetic energy, and their relationships. 2) It introduces the concepts of electric fields and electric potential, defining them and explaining how electric potential energy depends on charge and electric potential. 3) It then discusses the capacitance of parallel plates and spherical capacitors, defining capacitance and deriving the formula for capacitance of parallel plates based on physical considerations of the electric field and potential difference.

1. Rai Saheb Bhanwar Singh College
Nas.ganj

2. Work
• You do work when you push an object up a hill
• The longer the hill the more work you do: more
distance
• The steeper the hill the more work you do: more
force
The work W done on an object by an agent
exerting a constant force is the product of the
component of the force in the direction of the
displacement and the magnitude of the
displacement
dFW ||=

3. Work done by gravity
θcosFdW =
m
mg
d
θcosF
θ

4. Energy is capacity to do work
note Ep aka UG
• Gravitational Potential Energy
• Kinetic Energy
• Energy can be converted into other forms of
energy
• When we do work on any object we transfer
energy to it
• Energy cannot be created or destroyed
mghUG =
2
2
1
mvK =
GU∆−=∆Κ
GUKW ∆−=∆=

5. • A person lifts a heavy box of mass ‘m’ a
vertical distance ‘h’
• They then move a distance ‘d’, carrying the
box
• How much work is done carrying the box?
Quiz

6. Conversion of Gravitational
Potential Energy to Kinetic
Energy
m
mg
m
v
mghUG −=∆
2
2
1
mvK =∆
ghv
ghv
mghmv
2
2
2
1
2
2
=
=
=
Work done on object
h

7. What’s an electric field?
• A region around a charged
object through which another
charge will experience a force
• Convention: electric field
lines are drawn out of (+) and
into (-); so the lines will show
the movement of a “positive
test charge”
• E = F / q
• units are in N/C
+Q
+Q

8. Electric Potential Energy
charges also have electrical potential energy
E
EF Q=
+Q
+Q
d
FdW =
QEd=
QEdUe −=∆
v

9. Electric Potential Energy
• Work done (by electric field) on
charged particle is QEd
• Particle has gained Kinetic Energy
(QEd)
• Particle must therefore have lost
Potential Energy ∆U=-QEd

10. Electric Potential
The electric potential energy depends on
the charge present
We can define the electric
potential V which does not depend
on charge by using a “test” charge
EdQU 0−=∆
0Q
U
V
∆
=∆
Change in potential is
change in potential energy
for a test charge per unit
charge
Ed
Q
U
V −=
∆
=∆
0
for uniform field

11. Electric Potential
0Q
U
V
∆
=∆
compare with the Electric Field and Coulomb Force
0Q
F
E =
If we know the potential field this allows us to
calculate changes in potential energy for any
charge introduced
VQU ∆=∆ EF Q=

12. Electric Potential
Electric Potential is a scalar field
it is defined everywhere
but it does not have any direction
it doesn’t depend on a charge being there

13. Electric Potential, units
SI Units of Electric Potential
0Q
U
V
∆
=∆
EdV −=∆
Units are J/C
Alternatively called Volts (V)
We have seen
dVE /∆= Thus E also has units of V/m

14. Potential in Uniform field
E
+Q +Q
+Q
A B
C
0|| == dFWBC
|||| QEddFWAB ==
BCABAC WWW +=
||QEd=
||QEdUAC −=∆
d||
||EdVAC −=∆

15. Electric Potential of a single
charge
+
r
E
B
A
Advanced

16. Equi-potential Lines
Like elevation, potential can be displayed as contours
A contour diagram
Like elevation, potential requires a zero
point, potential V=0 at r=∞
Like slope & elevation we
can obtain the Electric Field
from the potential field
r
V
E
∆
∆
=

17. Potential Energy in 3 charges
∑=
r
Q
V
04
1
πεQ2
Q1
Q3
12
1
0
2212
4
1
r
Q
QVQU
πε
==
12
21
0
12
4
1
r
QQ
U
πε
=






++=+=
23
2
13
1
0
3123312
4
1
r
Q
r
Q
QUVQUU
πε
231312 UUUU ++=






++=
23
32
13
31
12
21
04
1
r
QQ
r
QQ
r
QQ
U
πε

18. Capacitors
A system of two conductors, each
carrying equal charge is known as
a capacitor

19. -
Capacitance of charged sphere
+Q
r=∞
V
Q
C
∆
= definition
R
r
Q
V
0 4
1
πε
+ = potential due to
isolated charge

20. Capacitors
-
+ +Q -Q
e.g. 1: two metal spheres
e.g. 2: two parallel sheets
Each conductor is called a plate

21. Capacitance
Capacitance…….. is a measure of the
amount of charge a capacitor can store
(its “capacity”)
Experiments show that the charge
in a capacitor is proportional to the
electric potential difference
(voltage) between the plates.

22. Units
V
Q
C
∆
= Thus SI units of capacitance are:
C/V
This unit is also known as the farad
after Michael Faraday
Remember that V is also
J/C so unit is also C2
J-1
1F=1C/V

24. Capacitance
The constant of proportionality C is
the capacitance which is a property
of the conductor
VQ ∆∝ VCQ ∆=
V
Q
C
∆
=
Experiments show that the charge in a
capacitor is proportional to the electric
potential difference (voltage) between the
plates.

25. Capacitance of parallel plates
+Q -Q
Intutively
The bigger the plates the
more surface area over
which the capacitor can
store charge C ∝ A
E
Moving plates togeth`er
Initially E is constant (no
charges moving) thus
∆V=Ed decreases charges
flows from battery to
increase ∆V⇒ C ∝ 1/dNever Ready
+
∆V

26. Batteries, Conductors & PotentialNeverReady
+
A battery maintains a
fixed potential
difference (voltage)
between its terminals A conductor
has E=0
within and
thus
∆V=Ed=0
∆V
∆V= 0

27. Capacitance of parallel plates
+Q -Q
Physically
E
Never Ready
+
EdV =∆
V
Q
C
∆
=
property of conductor
∆V

29. Rai Saheb Bhanwar Singh College
Nas.ganj