Download (a) Find the change in electric potential between points A and B.

25-1 Potential Differences and Electric
Potential
25-2 Potential Differences in a Uniform
Electric Field
25-3 Electric Potential and Potential
Energy due to Point Charges
Slide 1
Fig 25-CO, p.762
INTRODUCTION:
 Because the electrostatic force given by Coulomb’s law is
conservative, electrostatic phenomena can be conveniently
described in terms of an electric potential energy. This idea enables
us to define a scalar quantity known as electric potential.
 Because the electric potential at any point in an
electric field is a scalar function, we can use it to
describe electrostatic phenomena more simply than if
we were to rely only on the concepts of the electric field
and electric forces.
Slide 2
 When a test charge q0 is placed in an electric field E created by some other
charged object, the electric force Fe acting on the test charge is equal to q0E.
When the test charge is moved in the
electric field by some external agent, the
work done (W) by the electric field on the
q
charge is equal to the negative of the work
done by the external agent causing the
displacement ds.
Slide 3
Work (W )  Fe .ds  q0 E.ds
1. Work done (W) = Potential energy (U)
U  Fe .ds  q0 E.ds
2. Change in potential energy (U) between B and A is
given
B
U  U B U A   qo  E .ds
A
Potential energy (U) is a scalar quantity
Slide 4
3. The electric potential = potential (V).
The electric potential at any point in an
electric field is
4. The potential difference
U
V 
q0
V  VB  VA
between any
two points A and B in an electric field is defined as the change in potential
energy of the system divided by the test charge q0 :
U
V 
   E.ds
q0
A
B
Electric potential (V) is a scalar characteristic of an electric
field, independent of the charges that may be placed in the field.
However, when we speak of potential
referring to the charge–field system
Slide 5
energy (U), we are
Because electric potential is a measure of potential energy per unit charge,
the SI unit of both electric potential and potential difference is joules per
coulomb, which is defined as a volt (V):
U
Work
V 
q0 ch arg e
Volt x electron charge = electron volt ( eV)
Electron volt (eV), which is defined as the energy gains
or loses of an electron (or proton) by moving through a
potential difference of 1 V.
1 eV = 1.6 x10-19 C x 1 V = 1.60 x 10-19 J
Slide 6
25.2 Potential Deference in a uniform Electric Filed
a) When the electric field E is directed downward,
point B is at a lower electric potential than point A.
When a positive test charge moves from point A to
point B, the charge–field system loses electric
potential energy.
B
V  VB  VA    E . ds
A
B
   E ds cos 
A
B
  E  ds cos 0
V
Slide 7
A
 Ed
U  qo V   qo E d
Fig 25-2a, p.765
Slide 8
Equipotential Surface
uniform electric field
Find the electric
potential difference
VB –VA through the
path AB and ACB
AC = d = s cos θ
Slide 9
AC = d = s cos θ
Slide 10
Slide 11
An equipotential surface is any surface consisting of a
continuous distribution of points having the same electric
potential. Equipotential surfaces are perpendicular to
electric field lines.
Four equi-potential surfaces
Slide 12
Fig 25-4, p.766
A battery produces a specified potential difference between conductors
attached to the battery terminals. A 12-V battery is connected between two
parallel plates. The separation between the plates is d= 0.30 cm, and we
assume the electric field between the plates to be uniform.‫؟‬
Slide 13
Fig 25-5, p.767
A proton is released from rest in a uniform electric field that has a
magnitude of 8.0 x104 V/m and is directed along the positive x axis . The
proton undergoes a displacement of 0.50 m in the direction of E. (a) Find
the change in electric potential between points A and B.
(b) Find the change in potential energy of
the proton for this displacement.
H.W.: Use the concept of conservation of energy
to find the speed of the proton at point B.
Slide 14
Fig 25-6, p.767
B
V B V A    E .ds
A
q
q
E .ds  k e 2 r .ds  k e 2 ds cos 
r
r
q
 k e 2 dr
r
B
Slide 15
rB
V B V A
dr
   E dr   k e q  2
r
A
rA
V B V A
1
1
 k eq (  )
rB rA
Fig 25-7, p.768
Electric potential created by a point charge
If rB = r , rA = α , 1/ rA= 0 , The
electric potential created by a point
charge at any distance r from the
charge is
q
V  ke
r
Electric potential due to several point charges
For a group of point charges, we can write the total
electric potential at P in the form
P
q1
Slide 16
q2 q
3
q4
q5
qi
V  ke 
ri
Electric potential energy due to two charges
U  V q1
q1 q2
U  ke
r12
Slide 17
The total potential energy of the system of three
charges is
q1 q2 q1 q3 q2 q3
U  ke (


)
r12
r13
r23
U  ke 
Slide 18
qij
rij
Fig 25-11, p.770
Slide 19
Fig 25-12, p.771
Slide 20
Fig 25-12a, p.771
Slide 21
Slide 22
Slide 23
If the electric field E is in the x direction it will has
only one component Ex, then
Therefore,
Slide 24
Or E often is written as:
Slide 25
‫مثال ‪1‬‬
‫يعطي الجهد الكهربائي في منطقة ما بالمعادلة التالية‪:‬‬
‫اوجد المجال الكهربائي عند النقطة التي إحداثياتها‬
‫‪Slide 26‬‬
Slide 27
Homework (2)
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
q1 q2 q1 q3 q2 q3
U  ke (


)
r12
r13
r23
Slide 33
U  ke 
qij
rij
The potential gradients is :
Slide 34