Transcript Electrical Energy Potential

Electrical Energy Potential
• Consider a positive charge q located in an
electrical field of E that travels in one
dimension through Δx from A to B.
+
+ Aq
+
B -
Cont.
• The work done on the charge by the electric
field is given by WAB = qExΔx J
• This is valid for both +ve and -ve charges
influenced by a constant electrical field. As
electrical fields are vectors, direction of the
field and the corresponding displacement of
the charge must be indicated by a +ve or -ve
sign.
Cont.
• The work done is independent of the path
taken from A to B.
• Moving a charge in the opposite direction of
then field increases the objects potential
energy.
• Releasing the charge so that it may move
with the field converts its potential energy
to kinetic energy.
Consider Work-Energy Theorem
• Change in electric potential energy is a
change in work.
•
W = qExΔx = ΔKE
• The gain in kinetic energy is a loss of
electric potential energy
Electrical Potential
• The electric potential difference ΔV
between two points A and B is the change in
electric potential energy as a charge q
moves from A to B, divided by the charge q
• ΔV = VB- VA = ΔPE/q J/C or V(volt)
• Electric potential energy is a scalar quantity.
• ΔPE/q = ExΔx = V 1 N/C = 1 V/m
Cont.
• The above is true for a uniform electrical
field and a charge moving in one dimension.
High electrical potential is near or at the
+ve terminal, low potential is near or at the
-ve terminal.
• Released from rest a positive charge will
accelerate towards regions of low electrical
potential.
Consider a 12V car battery
• The battery maintains an electrical potential
of 12V across its terminals. The +ve
terminal is 12V higher in potential than the ve terminal.Every coulomb of +ve charge
that leaves the +ve terminal carries 12J. The
charge that moves through an external
circuit ( light) towards the -ve terminal
gives up 12J of electrical energy to the
external device.
Battery cont.
• When the charge reaches the -ve terminal
the potential is zero, the battery takes over
moving the charge from the -ve to the +ve
terminal thus restoring the potential. The
process then is repeated.
Electric Potential due to a Point
Charge
• The electric field of a point charge extends
through space as does its electric potential. The
zero point of electric potential is defined at an
infinite distance from the charge. The electric
potential at any distance is given by V = keq/r
• The electric potential of two or more charges is the
algebraic sum of the individual point charges’
potentials. (scalar quantities)
Potential Energy due to a Point
Charge
• Consider two charges being brought
together, the electric potential energy is
given by PE = keq1q2/r
• If the charges are the same sign the PE is
+ve. If they are of opposite sign s then PE is
–ve. That is –ve work must be done to
prevent the two charges from accelerating
together.
Potentials and Charged Conductors
• The electric potential energy between two
points is related to the potential difference
between those points.
• AS W = ΔPE and ΔPE = q (VB-VA)
then W = q (VB-VA)
• No net work is required to move a charge
between two points that are at the same
electric potential.
Cont.
• A conductor in electrostatic equilibrium has a net
charge that resides on the surface. The electric
field just outside the surface is perpendicular to
the surface. All points on the charged conductor in
electrostatic equilibrium are at the same potential
and the electric potential is constant everywhere
on the surface. The electric potential is constant
everywhere inside the conductor and is the same
as that on the surface.
The Electron Volt (eV)
• An electron volt is the kinetic energy gained
by an electron when it is accelerated
through a potential difference of 1V.
• AS 1V = 1 J/C and the charge on an
electron is 1.60x10-19 C then
1 eV = 1.60x10-19 C.V or J
Equipotential Surfaces
• This is a surface on which all points are at
the same potential. No work is required to
move a charge at constant speed on an
equipotential surface. Equipotentials are
lines drawn perpendicular to the electric
field lines at varying distances r from the
point source.
Capacitance
• A capacitor is a device that temporarily stores
electrical energy that can be reclaimed at a later
time. It consists of two parallel metal plates
separated by a distance d, each connected to one
of the terminals of an electrical source. The plate
connected to the +ve terminal losses electrons to
the source becoming +ve charged, +Q. The plate
connected to the –ve terminal gains these stripped
electrons becoming –ve charged, -Q.
Cont.
• The transfer of electrons stops when the
potential difference across the plates equals
the potential difference of the source.
• The capacitance C of the capacitor is the
ratio of the charge on a plate to the potential
difference between the plates.
C = Q/ΔV farad (F) = C/V
• Typical capacitance ranges from 1µF to 1pF
Cont.
• Capacitance is related to the area of the
plates A and the distance between them d
•
C = ЄoA/d
• The larger the plate and/or the smaller the
distance between them the larger the
capacitance.
• Capacitors store a large charge that can be
delivered quickly.
Symbols for Electrical Circuits
•
•
•
•
•
Electric source ( battery) + Capacitor
o
Light Bulb
Resistor
Wire of no or little resistance
Capacitors in Parallel
• Two capacitors connected as shown are said to be
connected in parallel. The left plates have the
same potential as do the right plates
• The total charge stored is Qeq = Q1 + Q2
• The equivalent capacitance Qeq of a parallel
combination is greater than the individual
capacitance.
• Ceq = C1 + C2
Capacitors in Series
• For a series connection the magnitude of charge
on the plates must be the same for all plates.
Regardless of the capacitance or how many are in
series, all plates connected to the +ve terminal will
have a positive charge and plates connected to the
–ve terminal will have a negative charge.
• The equivalent capacitance is given by
1/Ceq = 1/C1 + 1/C2 The equivalent capacitance
is always less than the individual capacitance.
Energy Stored in a Charged
Capacitor
• If the plates of a charged capacitor are
connected by a wire, the charge will transfer
from one plate to the other until both plates
are uncharged. Discharge may be seen as a
spark. When a capacitor is not charged both
plates are neutral, plates have the same
potential. Little work is required to transfer
a small charge ΔQ from one plate to the
other.
Stored Capacitance cont.
• Once a charge has been transferred a small
potential exists between the plates.
ΔV = ΔQ/C and any additional charge to be
transferred through a potential requires
work. The total work needed to fill a
capacitor is given by W = ½ Q ΔV
Energy stored = ½ QΔV = ½ C(ΔV)2 = Q2/2C
Cont.
• There is a limit to the capacity of a
capacitor. At a point the coulomb forces
between plates is so strong electrons jump
across the gap. Capacitors are usually
labeled with a maximum operating voltage.
• Ex Blinking lights A Defibrillator
Dielectrics
• A dielectric is an insulating material. Ex
plastic rubber. Placed between the plates of
a capacitor increases the capacity of the
capacitor by a factor of K, the dielectric
constant. Note K > 1 as C = Q/ΔV then
the increase in capacitance is given by
C = KQ/ΔV and C = KЄoA/d
Dielectrics cont.
• By decreasing d one can increase the
capacitance up to the limit until the
maximum electric field is established and
discharge will occur.
• This maximum field is called the Dielectric
Strength, for air this is 3x106 V/m Most
material have values greater than air.