Electrostatics

1
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)
• Charge

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.

4
Electrical Potential Energy
Recall thatpotential energyis zero at infinity8
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, youll 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 8 HighestEnergy ie. 0J
Lowest Energyie. -100J
Some Energyie. -50J
Q2
-
-
-
Q2
Q2



Highest Energyie. 100J
Some Energyie. 50J
At 8 LowestEnergy, 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 tozero 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 ?EP EPf - EPi
• W kQ1Q2/rf - kQ1Q2/ri
• W kQ1Q21/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
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, lets look at the
  total amount of energy a charge has
• ELECTRIC POTENTIAL

12
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
14
Electrical Potential

• Example Contd What is the potential difference
  between 1.5m and 5m?
• ?V V5 - V1.5
• ?V (-9x106V) - (-3x107V)
• ?V 2.1x107V

-5mC
V1.5
V5
5m
1.5m
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Electrical Potential

• From the previous example, consider the
  following
• ?V Vf - Vi
• ?V EPf/q - EPi/q
• ?V (EPf - EPi)/q
• ?V W/q
• W ?Vq

Work required tomove a chargefrom one
voltageto another
16
Electrical Potential

• Example Contd How much work does it take to
  move a 1µC charge from 1.5m to 5m?
• W ?Vq
• W (2.1x107V)(1x10-6C)
• W 21 J

1µC
1µC
1µC
-5mC
V1.5
V5
5m
1.5m
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Conclusions

• Electric Potential, Potential, Voltage
• Same Diff
• Measured in Volts
• V kQ/r
• W ?Vq
• Zero volts is sometimes called ground
• Symbol is