Chapter 22 : Electric potentialastronomy.swin.edu.au/~cblake/Topic5_Electricity_Part2.pdfย ยท โข...
Transcript of Chapter 22 : Electric potentialastronomy.swin.edu.au/~cblake/Topic5_Electricity_Part2.pdfย ยท โข...
Chapter 22 : Electric potential
โข What is electric potential?
โข How does it relate to potential energy?
โข How does it relate to electric field?
โข Some simple applications
Electric potential
โข What does it mean when it says โ1.5 Voltsโ on the battery?
โข The electric potential difference between the ends is 1.5 Volts
Electric potential
1.5 V230 V
100,000 V
So what is a volt?
Electric potentialโข The electric potential difference โ๐๐ in volts
between two points is the work in Joules needed to move 1 C of charge between those points
โข โ๐๐ is measured in volts [V] : 1 V = 1 J/C
๐๐ = ๐๐ ร โ๐๐
W = work done [in J]q = charge [in C]โV = potential difference [in V]
Electric potential
The 1.5 V battery does 1.5 J of work for every 1 C of charge flowing round the circuit
๐๐ = ๐๐ ร โ๐๐
โข The electric potential difference โ๐๐ in volts between two points is the work in Joules needed to move 1 C of charge between those points
Potential energyโข What is this thing called โpotentialโ?
โข Potential energy crops up everywhere in physics
Potential energyโข Potential energy U is the energy stored in a system
(when work is done against a force)
โข e.g. force of gravity โฆ๐น๐น = ๐๐๐๐
โ
๐๐ = ๐น๐น ร โ
Work = Force x Distance
= ๐๐๐๐โ
โ ๐๐ = ๐๐๐๐โ
๐น๐น
Potential energyโข Potential energy may be released and converted
into other forms (such as kinetic energy)
Work is done, increasing the potential energy
Potential energyโข Potential energy difference is the only thing that
matters โ not the reference (or zero) level
โข For example, applying conservation of energy to a mechanics problem:
๐พ๐พ๐พ๐พ๐๐๐๐๐๐๐๐๐๐ + ๐๐๐พ๐พ๐๐๐๐๐๐๐๐๐๐ = ๐พ๐พ๐พ๐พ๐๐๐๐๐๐๐๐๐๐๐๐๐๐ + ๐๐๐พ๐พ๐๐๐๐๐๐๐๐๐๐๐๐๐๐
Final energy = Initial energy
๐พ๐พ๐พ๐พ๐๐๐๐๐๐๐๐๐๐ = ๐พ๐พ๐พ๐พ๐๐๐๐๐๐๐๐๐๐๐๐๐๐ + (๐๐๐พ๐พ๐๐๐๐๐๐๐๐๐๐๐๐๐๐โ๐๐๐พ๐พ๐๐๐๐๐๐๐๐๐๐)
Difference in potential energy
Potential energyโข Potential energy difference doesnโt depend on the
path โ only on the two points A and B
Potential energyโข Potential energy U is the energy stored in a system
โ second example
โข e.g. stretching a spring โฆ ๐น๐น = ๐๐๐๐
๐๐
๐๐ = ๏ฟฝ๐๐๐๐ ๐๐๐๐
Work = Force x Distance
= 12๐๐๐๐
2
โ ๐๐ = 12๐๐๐๐
2
๐น๐นForce is varying with distance!
Electric potentialโข e.g. moving a charge through an electric fieldโฆ
๐น๐น๐พ๐พ
๐น๐น = โ๐๐๐พ๐พ
Work = Force x Distance = โ๐๐๐พ๐พ โ๐๐๐๐ = ๐น๐น โ๐๐
โข Potential difference โ๐๐ is work needed to move 1C of charge: ๐๐ = ๐๐ โ๐๐
โข Equate: ๐๐ โ๐๐ = โ๐๐๐พ๐พ โ๐๐
๐๐(minus sign because the force is opposite to E) โ๐๐
๐พ๐พ = โโ๐๐โ๐๐
Electric potentialโข Electric field is the gradient of potential ๐พ๐พ = โโ๐๐
โ๐ฅ๐ฅ
High V Low V๐พ๐พ ๐๐
๐๐
๐๐
โข Positive charges feel a force from high to low potential
โข Negative charges feel a force from low to high potential
Two parallel plates have equal and opposite charge. Rank the indicated positions from highest to lowest electric potential.
1 2 3 4
0% 0%0%0%
+ + + + + + + + + + + + + + + +
- - - - - - - - - - - - -โขA
โขB
โขC
โขD
1. A=C, B=D2. A, B, C, D3. C, D=B, A4. A, B=D, C
Electric potentialโข Analogy with gravitational potential
๐๐
๐๐
Gravitationalpotential difference exerts force on mass
Electric potential difference exerts force on charge
๐๐
Electric potential
High V Low V๐พ๐พ
โข The dashed lines are called equipotentials (lines of constant V)
โข Electric field lines are perpendicular to equipotentials
โข It takes no work to move a charge along an equipotential (work done = ๐๐๐๐ = ๏ฟฝโ๏ฟฝ๐น.๐๐๐๐ =๐๐๐พ๐พ.๐๐๐๐ = 0)
โข Electric field is the gradient of potential ๐พ๐พ = โโ๐๐โ๐ฅ๐ฅ
โข Summary for two plates at potential difference V
Electric potential
๐๐
๐พ๐พ โข Electric field is the potential gradient
โข Work W to move charge q from โve to +ve plate
๐พ๐พ =๐๐๐๐
๐๐ = ๐๐ ๐๐
โข The electric potential difference โ๐๐ between two points is the work needed to move 1 C of charge between those points
โข This work is also equal to the potential energy difference โ๐๐ between those points
โข Potential V = potential energy per unit charge U/q
Link to potential energy
๐๐ = ๐๐ ร โ๐๐
โ๐๐ = ๐๐ ร โ๐๐
An electron is placed at โXโ on the negative plate of a pair of charged parallel plates. For the maximum work to be done on it, which point should it be moved to?
1 2 3 4 5 6
0% 0% 0%0%0%0%
+ + + + + + + + + + + + + + + +
- - - - - - - - - - - - -โขX
โขA โขC
โขB
โขD
1. A2. B3. C4. D5. A or C6. C or D
โข What is the electric potential near a charge +Q?
+q
+Q
๐น๐น =๐๐ ๐๐ ๐๐๐๐2
๐๐
Work = Force x Distance
Force is varying with distance, need integral!
๐๐ = ๏ฟฝโ
๐๐๐น๐น ๐๐๐๐ = ๏ฟฝ
โ
๐๐โ๐๐ ๐๐ ๐๐๐๐2 ๐๐๐๐ =
๐๐ ๐๐ ๐๐๐๐
Potential energy ๐๐ = ๐๐ ๐๐ ๐๐๐๐
Electric potential ๐๐ = ๐๐๐๐
= ๐๐ ๐๐๐๐
Electric potential
+q
+Q๐๐
Electric potential ๐๐ = ๐๐ ๐๐๐๐
Electric potentialโข What is the electric potential near a charge +Q?
Electric potentialExercise: a potential difference of 200 V is applied across a pair of parallel plates 0.012 m apart. (a) calculate E and draw its direction between the plates.
The electric field is the gradient in potential
๐พ๐พ =โ๐๐โ๐๐
=200
0.012 = 1.7 ร 104 ๐๐ ๐๐โ1 [๐๐๐๐ ๐๐ ๐ถ๐ถโ1]
๐พ๐พ๐๐ = 200
๐๐ = 0
+ve plate
-ve plate
Electric potentialExercise: a potential difference of 200 V is applied across a pair of parallel plates 0.012 m apart. (b) an electron is placed between the plates, next to the negative plate. Calculate the force on the electron, the acceleration of the electron, and the time it takes to reach the other plate.
e = 1.6 x 10-19 C; me = 9.1 x 10-31 kg
๐พ๐พ+ve plate
-ve plateโ๐๐
Force ๐น๐น = ๐๐๐พ๐พ = (โ1.6 ร 10โ19) ร (1.7 ร 104) = โ2.7 ร 10โ15 ๐๐
๐น๐น = ๐๐๐๐ Acceleration ๐๐ = ๐น๐น๐๐
=2.7 ร 10โ15
9.1 ร 10โ31= 3.0 ร 1015 ๐๐ ๐ ๐ โ2
๐๐ = 12๐๐๐ก๐ก
2 Time ๐ก๐ก = 2๐๐๐๐
๐ก๐ก =2 ร 0.0123.0 ร 1015 = 2.8 ร 10โ9 ๐ ๐
Electric potentialExercise: a potential difference of 200 V is applied across a pair of parallel plates 0.012 m apart. (c) calculate the work done on the electron as it travels between the plates.
e = 1.6 x 10-19 C; me = 9.1 x 10-31 kg
๐พ๐พ+ve plate
-ve plateโ๐๐
The potential difference is the work done on 1C charge
Work ๐๐ = ๐๐๐๐ = 1.6 ร 10โ19 ร 200 = 3.2 ร 10โ17 ๐ฝ๐ฝ
Chapter 22 summary
โข Electric potential difference V is the work done when moving unit charge: ๐๐ = ๐๐๐๐
โข The electric potential energy is therefore also given by: ๐๐ = ๐๐๐๐
โข The electric field is the gradient of the potential: ๐พ๐พ = โโ๐๐/โ๐๐
โข Charges feel a force from high electric potential to low potential