Transcript 24-2: Electric potential energy

Chapter 24: Electric Potential
Introduction: Why will we be introducing the electrostatic
potential (V) and electric potential energy (U)?
Because they are scalars!! not vectors like F and E.
24-2: Electric potential energy
Coulomb’s law looks like the gravitation law. Hence, it is
conservative.
What does it mean for a force or field to be conservative?
The work done by the force is independent of path!
We can assign a potential energy (U) for the electric force!
DU = -W
where W is the work done by the electric force field.
If we take U∞ = 0 then,
U = - W∞
The potential energy of a charge at a point is
equal to the negative of the work done by the field
in bringing the charge from infinity to that point.
24-3: Electric Potential (V): is the potential energy per unit charge.
V = U/q
DV = DU/q = -W/q
V = - W∞/q
Note that the work you apply to a charge is the negative of the work
that the field applies on the charge (when there is no change in
kinetic energy). See the work energy theorem!
DV = Wapplied/q
or
Wapplied = q DV
The units of J/C is defined to be the volt (V).
For electric fields we can use: N/C or V/m.
What is the electron-volt?
How much energy is an eV?
24-4: Equipotential surfaces (EP)
Adjacent points that have the same electric
potential form and equipotential surface.
W = 0 in going from one point to another on
the same EP (regardless of path).
What is EP for a spherical charge
distribution?
What is EP for a uniform field?
E is always perpendicular to EP. (why?)
24-5: Calculating the potential from the field:
f
 
V f  Vi   E ds

i
What happens to the potential
when we move a distance d along
the electric field?
Solve check point 3:
What is the direction of the field?
In which process to we (the agent) do most work?
24-6: Potential due to a Point Charge:
q
1 q
V k 
r 40 r
Notice that:
1. V is a scalar (much easier to handle
than a vector!)
2. V can be positive or negative!
With the understanding
that V∞ = 0
24-7: Potential due to a Group of Point Charges:
V
V
i
i

1
40
n

i 1
qi
ri
Solve check point 4:
Rank the arrangements according to the net electric potential
produced at point P due by the protons.
24-8: Potential due to an Electric Dipole:
p cosq
V
40 r 2
1
What is r?
What is p?
What is q?
What is the induced dipole moment, and
what relation does it has with polarization?
24-10: Calculating the field from the potential :
E s   V
s
Solve check point 6: What is the direction of the electric field in the
three situations? Which has the greatest magnitude?
24.11: Electric Potential Energy of a System of Point Charges:
The electric potential energy of a system of fixed point charges is
equal to the work that must be done by an external agent to
assemble the system, bringing each charge from an infinite
distance.
For a single charge: U = 0
For two charges (q1&q2) a distance r apart:
U = k q1 q2/ r
(can you prove it?)
For three charges (q1, q2 and q3):
U = k q1 q2/r12 + k q1 q3/r13 + k q2 q3/r23
What about for four charges?
Solve sample problem 25-36:
(a) What is the electric potential energy of two electrons
separated by 2 nm.
(b) If the separation increases, does the potential energy
increase or decrease?
24.12: Potential of a Charged Isolated Conductor:
The electric potential of a charged conductor is constant.
Can you explain why?!
What happens if a conductor is placed in an electric field?
1- DV = 0 in and on the conductor
2- The free charges in the conductor will
redistribute itself in order to create an (internal)
electric field that cancels the external (applied)
field. Also, the field at the surface is perpendicular
to the surface.
How can you shield an instrument (or a person!!) from an
electric field?
Place it/ him inside a conductor.
So, if you see lighting, jump into the car!!
Physics can save your life (Allah Willing) 