Transcript Document 7835088

Electrostatics
Electric Potential Energy
Objectives
Define electric potential energy and change in
electric potential energy
Solve 2 point charge problems at rest involving:
 Electric potential energy
 Charge
 Distance of separation
Moving 2 point charge problems involving:
 Change in electric potential energy
 Distance of separation (initial and final)
 Charge
Electrical Potential Energy
FE
Recall equation for electrical force:
FE = kQ1Q2/r²
When we were looking at
gravitational forces, how did we
find work done?
Area under the graph.
r
Electrical Potential Energy
kQ1Q2
EP 
r
FE
Recall that
potential energy
is zero at infinity
∞

r
Electrical Potential Energy
EP = kQ1Q2/r
When using the potential energy equation, keep
the following in mind:
Amount of potential energy due to separation
of two charged particles by distance “r”.
Include the signs of the charged particles
Drop the - sign
Electrical Potential Energy
EP = kQ1Q2/r
Drop the - sign, you’ll see!
A. A + particle has its highest energy when close to
another + particle
B. A - particle has its highest energy when far from a +
particle
C. Oppositely charged particles have low energy when
they are close together
At ∞ Highest
Lowest Energy
ie. -100J
+
+ Q2
Q1 Highest Energy
ie. 100J
Some Energy
ie. -50J
+ Q2
Some Energy
ie. 50J
Energy ie. 0J
- Q2
+
At ∞ Lowest
Energy, ie. 0J
Electrical Potential Energy Ex 1
How much potential energy does a 1mC charge
have when it is 1m away from a 5C charge?
EP = kQ1Q2/r
EP = (9x109Nm²/C²)(5C)(0.001C)/(1m)
EP = 4.5x107J
Relative to
zero at infinity
1mC
5C
1m
Electrical Potential Energy Ex 2
Same 2 particles, how much work is necessary to move
the 1mC charge to 1.5m away?
W = ΔEP = EPf - EPi
W = kQ1Q2/rf - kQ1Q2/ri
W = kQ1Q2[1/rf - 1/ri]
W = (9x109)(5)(0.001)[1/(1.5m) - 1/(1m)]
W = -1.5x107J
-, so work has been done by charges
(energy & work are not vectors)
5C
1mC
1.5m
1mC
Conclusions
Potential Energy: EP = kQ1Q2/r
Like charges experience a + potential energy
that increase the closer they are together
Opposite charges experience a - potential
energy that decreases the closer they are
together
Particles experience zero potential energy
when they are infinitely far apart from one
another
Electrostatics
Electric Potential
Voltage
Electrical Potential
We have already looked at the amount of
energy a charge has:
E = kQ1Q2/r
But that is rarely useful, let’s look at the
total amount of energy a charge has:
ELECTRIC POTENTIAL
Electrical Potential
Electric Potential is also sometimes called just simply
“Potential”
Symbol is “V” (Named after Volta)
Measured in Volts (J/C)
It is the amount of work required to move a unit of
charge from point A to point B
V = EP/q
V = (kQq/r) / q
V = kQ/r
Alessandro Volta - Built the first battery
Electrical Potential
Example: Find potential of the -5mC charge at
1.5m and at 5m away?
V = kQ/r
V1.5 = (9x109J)(-0.005C)/(1.5m)
 V1.5 = -3x107V
V5 = (9x109J)(-0.005C)/(5m)
 V5 = -9x106V
-5mC
V1.5
1.5m
V5
5m
Electrical Potential
Example Cont’d: What is the potential
difference between 1.5m and 5m?
ΔV = V5 - V1.5
ΔV = (-9x106V) - (-3x107V)
ΔV = 2.1x107V
ΔV
-5mC
V1.5
1.5m
V5
5m
Electrical Potential
From the previous example, consider the
following:
ΔV = Vf - Vi
Work required to
move a charge
ΔV = EPf/q - EPi/q
from one voltage
to another
ΔV = (EPf - EPi)/q
ΔV = W/q
W = ΔV*q
Electrical Potential
Example Cont’d: How much work does it take to
move a 1μC charge from 1.5m to 5m?
W = ΔV*q
W = (2.1x107V)(1x10-6C)
W = 21 J
-5mC
1.5m
1μC
1μC
V1.5
V5
5m
Conclusions
Electric Potential, Potential, Voltage
Same Diff
Measured in Volts
V = kQ/r
W = ΔV*q
Zero volts is sometimes called ground
Symbol is