Physics 1051 Lecture 14. Electric Potential. Physics General Physics II Oscillations, Waves and Magnetism

Transcription

1 Physics 1051 Lecture 14 Electric Potential

2 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 2

3 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 3

4 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 We don't normally look at this Gravitational Potential one for Gravitational and you've never seen it before. We will for Electrical! 4

5 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 Work done ON the OBJECT BY the FIELD W con = U 5

6 Definition of Work For one step in finding Electric Potential Energy you will need to know the definition for work. For a constant Force Physics 1020 W =F x x cos version (Δx instead of d) W = F r For a variable Force - GENERAL dw = F d r x W = f x i F d r Infinitesimal work over infinitesimal displacement e.g use for work done by a spring force 6

7 Potential Energy Examples Gravitational Spring 7

8 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 B U = A F e d s For some reason we using ds for infinitesimal position instead of dr B U = q 0 E d s A 8

9 Change in Electric Potential Energy B U =q 0 A E d s Quantity Type SI Unit Scalar Joule (J) q 0 is charge of test particle E Electric Field (due to source particles) that test particle is in d s is some infinitesimal displacement along the field between positions and s A REMEMBER; sign of charge goes in here since no absolute value sign s B 9

10 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... 10

11 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 = U q 0 V = 1 B q q 0 E d 0 s A 11

12 FORMULA Potential Difference B V = A E d s Quantity Type SI Unit Scalar Volt (V) equiv to J/C E Electric Field (due to source particles) that test particle is in d s is some infinitesimal displacement along the field between positions and s A Other unit: The Electron Volt 1eV = 1e 1V = C 1 J /C = s B 12

13 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 P zero V P = E d s 13

14 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 V? (The potential in each case is measured relative to a common reference point.) 14

15 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. 15

16 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? B V = E d s A B V = E A V = E r d s E comes outside because it is uniform and this constant along ds 16

17 Uniform Electric Field - Potential Energy Difference We can use this formula for Electric Potential Difference to find Electric Potential Energy Difference V = E r Starting relation between Electric Potential Difference and Electric Potential Energy Difference U =q 0 V U =q 0 E r U =q 0 E r 17

18 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! 18

19 What to Equipotential Field Lines Look Like? The potential difference formula for Uniform Electric Field will tell us V = E r=e r cos 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 W con = U =q 0 V =q 0 0 =0 19

20 Specific Case of Uniform Electric Field - Displacement is Parallel to Field Let's look at potential difference and potential energy difference V = E r=e r cos V =E r cos For this case, what is theta? Theta is zero. V =E r cos0 V =E d 20

21 Potential Difference and Potential Energy Difference Potential Difference V =E d Can find potential energy change: U =q 0 V U =q 0 Ed U =q 0 Ed See Figure 20.1 Looks like mgh 21

22 Potential Energy! When a positive charged particle moves in same direction of Electric Field, the potential energy of the chargefield system decreases. When a negative charged particle moves in the opposite direction of Electric Field, the potential energy of the chargefield system decreases. U =q 0 Ed See Figure

23 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 V. If the distance between these plates is 1.50 cm. What is the magnitude of the uniform electric field in this region? 23