1. Electric Potential Energy
Electrostatics
Electric Potential Energy

2. 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)

3. Electrical Potential Energy
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. FE r

4. Electrical Potential EnergyFE r
Recall that potential energy is zero at infinity ∞

5. 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

6. Electrical Potential Energy
EP = kQ1Q2/r
Drop the - sign, you’ll see!
A + particle has its highest energy when close to another + particle
A - particle has its highest energy when far from a + particle
Oppositely charged particles have low energy when they are close together
At ∞ Highest Energy ie. 0J
Lowest Energy ie. -100J
Some Energy ie. -50J + Q1 - - - Q2 Q2 Q2 + + +
Highest Energy ie. 100J
Some Energy ie. 50J
At ∞ Lowest Energy, ie. 0J

7. 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 5C
1mC 1m

8. 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)
1mC
1mC 5C
1.5m

9. 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

10. Electric Potential Voltage
Electrostatics
Electric Potential
Voltage

11. 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

12. Alessandro Volta - Built the first battery
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

13. 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 5m V5

14. 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 V5
1.5m 5m

15. Work required to move a charge from one voltage to another
Electrical Potential
From the previous example, consider the following:
ΔV = Vf - Vi
ΔV = EPf/q - EPi/q
ΔV = (EPf - EPi)/q
ΔV = W/q
W = ΔV*q
Work required to move a charge from one voltage to another

16. 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
1μC
1μC
1μC
-5mC
V1.5 V5
1.5m 5m

17. Conclusions Electric Potential, Potential, Voltage Same Diff
Measured in Volts
V = kQ/r
W = ΔV*q
Zero volts is sometimes called ground
Symbol is