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Physics 1051 - General Physics IIOscillations, Waves and Magnetism

Physics 1051 – Lecture 14

Electric Potential

10/06/10Physics 1051 – Bill Kavanagh

2 Physics 1051 - General Physics IIOscillations, Waves and Magnetism

Lecture 14 - Contents

20.0 Describing Electric Phenomenon using Electric Potential

20.1 Electric Potential Difference and Electric Potential

20.2 Potential Difference in a Uniform Field



20.0 Describing Electric Phenomenon using Electric Potential

● We have already discussed Electric phenomenon that result from charged objects

● We have described it so far with two main quantities− Electric Force− Electric Field (and Electric Flux)

● Now, we will look at two other quantities that describe the same Electric phenomenon− Electric Potential Energy − Electric Potential



Gravitational Analogy:Potential?

● Like with Force and Field for Electric was analogous to Gravitational, so too is Potential Energy and

● For gravity we have− Gravitational Force− Gravitational Field (and Electric Flux)

● We also have− Gravitational Potential Energy − Gravitational Potential

We don't normally look at this one for Gravitational and you've never seen it before. We will for Electrical!



Conservative Forces - Potential and Potential Energy

● Note: A conservative force is defined in Chapter 7. You should review it!

● Conservative force property (that follows from definition) is very important here to the idea of Potential Energy:− Conservative force between a test object and the

source; energy is stored in the system.− Associated equation is Equation 7.14

W con=−UWork done

ON the OBJECT BY the FIELD



Definition of Work

● For one step in finding Electric Potential Energy you will need to know the definition for work.− For a constant Force

− For a variable Force - GENERAL

W=∫xi

x f

F⋅d r

W=F⋅r

W=F x x cos Physics 1020 version (Δx instead of d)

e.g use for work done by a spring force

dW=F⋅d rInfinitesimal work over infinitesimal displacement



Potential Energy Examples

● Gravitational

● Spring



20.1 Electric Potential Difference and Electric Potential

● Since the Electric Force is conservative, we can apply general method for finding change in Potential Energy from point A to B:

U=−W con

U=−∫A

B

F e⋅d s

U=−∫A

B

q0E ⋅d s

For some reason we using ds for infinitesimal position instead of dr



Change in Electric Potential Energy

− is charge of test particle− Electric Field (due to source particles) that test

particle is in− is some infinitesimal displacement along the

field between positions and

U=−q0∫A

B

E⋅d sQuantity Type Scalar

SI Unit Joule (J)

q0

REMEMBER; sign of charge goes in here since no absolute value sign

E

d ss A s B



Can you have potential energy with only one Charge?

● We asked a similar question when we discussed Electric Force and discovered the quantity Electric Field

● Is there still a electric potential energy if there is only one particle?− No. But there is something Electric Potential!!!

● Even if we only have one particle (let's say a source particle), the Electric phenomenon is still present.

● Let's discover Electric Potential...



Electric Potential

● Electric Potential is like electric potential energy but is independent of the test particle and only depends on the source particle(s).

● Similar to what we did to find Electric Field, we will divide change in Electric Potential Energy by the charge on the test particle

V =Uq0

V = 1q0−q0∫

A

B

E⋅d s



FORMULA – Potential Difference

− Electric Field (due to source particles) that test particle is in

− is some infinitesimal displacement along the field between positions and

● Other unit: The Electron Volt−

V =−∫A

B

E⋅d sQuantity Type Scalar

SI Unit Volt (V) equiv to J/C

E

d ss A s B

1eV =1e1V=1.60×10−19 C 1 J /C =1.60×10−19



Potential

● We have just defined potential difference without defining potential.

● It turns out, the potential at a spot requires picking a reference zero potential.− This is just like having to pick a zero gravitational

potential energy, usually the earth's surface.

● For Electric potential we almost always pick infinity (as far away from source charge) as zero

V P=−∫∞

P

E⋅d s



Example

Problem 20.2, page 674 How much work is done (by a battery, generator, or some other source of potential difference) in moving Avogadro's number of electrons from an initial point where the electric potential is 9.00 V to a point where the potential is -5.00 V? (The potential in each case is measured relative to a common reference point.)



20.2 Potential Difference in a Uniform Field

● After having looked at the most general case of non uniform electric field, we can look at the uniform electric field case.

● We will now derive two specific formula's within this section for Uniform Fields.

● Note: These two formula's are only examples, are not on the formula sheet and you would be expected to know how to figure this out on your own from the general case.



Uniform Electric Field -Potential Difference

● Recall what a uniform electric field is:− Constant in space and time!

● Now, what can we do to general potential difference formula?

V =−E⋅∫A

B

d s

V =−∫A

B

E⋅d s

V =−E⋅r

E comes outside because it is uniform and this constant along ds



Uniform Electric Field -Potential Energy Difference

● We can use this formula for Electric Potential Difference to find Electric Potential Energy Difference−

● Starting relation between Electric Potential Difference and Electric Potential Energy Difference

V =−E⋅r

U=q0V

U=q0 −E⋅r U=−q0

E⋅r



Equipotential Lines!

● This formula for Potential Energy Difference allows is to visualize something known as equipotential lines.

● Equipotential Lines: A line along which the potential is equal i.e. The potential doesn't change i.e.

● What does this mean for potential difference?− The potential difference is zero!



What to Equipotential Field Lines Look Like?

● The potential difference formula for Uniform Electric Field will tell us

● When is this zero?− When theta is 90º i.e. Field Line is Perpendicular to the

displacement

● Equipotential Lines are perp. to Field Lines● No work moving a charge along Equipotential Line

V =−E⋅r=−E r cos

W con=−U=q0V =q00=0



Specific Case of Uniform Electric Field - Displacement is Parallel to Field

● Let's look at potential difference and potential energy difference

● For this case, what is theta?− Theta is zero.

V =−E⋅r=−E r cos

V =−E r cos

V =−E r cos0V =−E d



Potential Difference and Potential Energy Difference

● Potential Difference

● Can find potential energy change:

V =−E d

U=q0V

U=q0−Ed

U=−q0 Ed

Looks like mgh

See Figure 20.1



Potential Energy!

● When a positive charged particle moves in same direction of Electric Field, the potential energy of the charge-field system decreases.

● When a negative charged particle moves in the opposite direction of Electric Field, the potential energy of the charge-field system decreases.

U=−q0 EdSee Figure 20.1



Example

Problem 20.4, page 674 The difference in potential between the accelerating plates in the electron gun of a TV picture tube is about 25 000 V . If the distance between these plates is 1.50 cm. What is the magnitude of the uniform electric field in this region?

electric potential - physics.mun.cawkavanagh/courses/phys1051/notes/lecture14... · physics 1051...

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