Download Electric Potential and Electric Energy

Electric Potential and Electric
Energy; Capacitance
Adapted from Giancoli Physics
Potential Energy
• Measured as a
difference of potential
energies rather than
as an absolute value.
– Electric potential
energy refers to the
change in potential
energy as charge
moves from A to B.
Electric Potential Energy
• The negative of the work done by the
electric field to move the charge.
• Because it is the difference between the
points that is measured, EITHER point
can be zero.
Electric Potential
• V is defined as the quotient of potential
energy to charge, such that
Ua
Va 
q
• Also, Vab= Va - Vb = 
Wba
q
*Measured
In Volts
Electric Potential
•Usually called VOLTAGE.
•Electric Potential is a measure of Electric
Potential Energy PER CHARGE.
•V = PE/q
More Energy Less Energy
+
+
+
Electric Potential Energy Vs. Electric Potential
More Energy
Per charge
+
+
Higher Voltage
More Total Energy
because more
“less energy per
charge” charges
+++
++ +
+ +
Lower Voltage
Voltage
• A measure of electric potential energy
per unit of charge.
• 1 V = 1J/1C
• ∆U = Ub - Ua = qVba
Relation Between Potential
and Field
• For a uniform electric field:
• E = Vba/d for a positive charge q moved to a
point b to a point a separated by d meters.
• Electric field is a vector with units V/m or
N/C
• Electric Potential is a scalar with units V or
J/C
The Electron-Volt
• A unit of energy on the microscopic
level.
• 1 eV = 1.6 x 10-19 J (sound familiar?)
• The energy gained or lost by an
electron traveling across a 1V
difference.
Electric Potential Due to Point
Charges
• Assuming V = 0 when d = ∞, V at
distance r from point Q is given by
• V = kQ/r
• Combined electric potential for several
point charges is given by the sum of
their individual potentials.
– (Note that sign for each potential must
equal their charge) Hooking up batteries backward.
Electric Dipoles
• Consists of two equal but opposite point
charges separated by a distance.
• Water is an electric dipole.
Capacitance
• Capacitor is a charge storing device.
• Made of two conducting parallel plates
separated by a small layer of air or a thin film.
• The charge quantity on each plate Q is
proportional to the Voltage applied.
Q = VC. C is Capacitance (depends on Capacitor)
• C is a function of the distance between
plates and the area of each, A, such
that: C = ε0A/d
(ε = epsilon)
C = ε (0)A/d
• ε0 = Permittivity of free space
• ε0 = 8.85 x 10-12 C2/Nm2
– Permittivity is ability of an object to hold
electric energy in an electric field.
• Unit of Capacitance is C/V or the farad.
(microfarad/picofarad)
Charging a Capacitor
• When a battery is
connected to a series
resistor and capacitor, the
initial current is high as the
battery transports charge
from one plate of the
capacitor to the other. The
charging current
asymptotically approaches
zero as the capacitor
becomes charged up to the
battery voltage. Charging
the capacitor stores energy
in the electric field between
the capacitor plates.
Dielectrics
• Materials used to separate the plates of
a capacitor.
– The dielectric constant: a ratio of
Capacitance ranging from 1-10 comparing
a capacitor with a material between the
plates to a capacitor with a vacuum
between the plates.
C2
K
C1
Some Dielectric Constants
Material
Dielectric Constant
(K)
Proportionality
Constant (k)
Air
1.0
8.9 x 109
Paraffin
2.2
4.1 x 109
Polyethylene
2.3
3.9 x109
Rubber
2.8
3.2 x 109
Mica
6.0
1.5 x 109
Glass
8.0
1.1 x 109
Why Use a Dielectric?
• If charge grows too high between two plates,
the capacitor could do damage to equipment.
• Inserting a dielectric lowers the capacitance
of the conductors.
• Polarized or temporarily polar bodies lower
the potential.
+
+
+
+
+
_
_
_
_
_
+
+
+
+
+
_ +
_ +
_ +
_ +
_
_
_
_
_
The Leyden Jar
• A simple capacitor.
• Used to store and
release charge.
Let’s build one!