Chapter 28
description
Transcript of Chapter 28
Phys 133 – Chapter 30 1
Chapter 28
Electric Potential
Phys 133 -- Chapter 29 2
Looking ahead
New force (Chapter 25)
New potential energy (Chapter 28)
Phys 133 -- Chapter 29 3
Electric Potential Energy (Uelec)
• Potential energy ~ Gravitational ~ Uniform electric field~ Point charge
Phys 133 -- Chapter 29 4
Gravitational potential (energy)Defined
Then defined
For the gravitational force
In general
Phys 133 -- Chapter 29 5
Uniform field: Electric potential energy
where
Phys 133 -- Chapter 29 6
s
Uniform field: Electric potential energy
s
Direction of lower potential energy depends on type of charge
Lower potential energyLower potential energy
Positive charge Negative charge
Phys 133 -- Chapter 29 7
Do Workbook 29.6
Phys 133 -- Chapter 29 8
A proton is released from rest at the positive plate of a parallel plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 50,000 m/s. What will be the speed if the experiment is repeated with double the amount of charge on the capacitor plates?
(Ans: 7.07x104 m/s)
Problem 29.3
Phys 133 -- Chapter 29 9
Electrical Potential Energy of Two Point Charges
where
Phys 133 -- Chapter 29 10
Question
b) Two point charges (+/- Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?
a) Two point charges (both +Q) have their separation increased. Does the electric potential energy of the system (A) increase, (B) decrease or (C) remain the same?
Phys 133 -- Chapter 29 11
Question ans
Like chargesOpposite charges
Phys 133 -- Chapter 29 12
Do Workbook 29.3
Phys 133 -- Chapter 29 13
An electron (q=-e) is sent from very far away towards a charged sphere (Q=-0.25 nC). It gets to a distance of 1.10 mm from the center of the sphere before turning around.
What is the initial speed of the electron?
(Ans: 2.68x107m/s)
What was the speed of the same electron with same initial conditions when it was 2.20 mm away?
e=1.6x10-19C, me=9.1x10-31 kg, K=9x109 Nm2/C2
Problem
Phys 133 -- Chapter 29 14
Problem ans
Phys 133 -- Chapter 29 15
Electric Potential (Velec)• Potential
~ Gravitational ~ Uniform electric field~ Point charge
Phys 133 -- Chapter 29 16
Electric Potential (Velec)
Potential only depends on source charges
Charge creates potential
define
Look at•Gravitational •Uniform electric field•Point charge
Phys 133 -- Chapter 29 17
Gravitational Potential
environmentobject
Environment only
Phys 133 -- Chapter 29 18
Electric potential capacitor
s0
(from before)
environmentobject
Environment only
Phys 133 -- Chapter 29 19
Capacitor: potential representations
Phys 133 -- Chapter 29 20
Draw V(x) for the two equipotential surfaces
Draw U(x) for a proton in these potentialsDraw U(x) for an electron in these potentials
Phys 133 -- Chapter 29 21
Workbook 29.18b extensionA proton is at x=0, moving to the right with 5x10-18 J of kinetic energy. What is its kinetic energy at point a?
What if it were an electron?
Phys 133 -- Chapter 29 22
Workbook 29.18b extension ans
proton electron
Not enough energy to reach a
Phys 133 -- Chapter 29 23
a) In the figure which capacitor plate, left or right, is the positive plate?
b) What is the electric potential energy of a proton at the midpoint of the capacitor?
c) What is the electric field strength inside the capacitor?
Problem 29.21 Modified
In general
d) What is the electric field strength inside the capacitor in terms of and o?
e) What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates?
Phys 133 -- Chapter 29 24
Only potential difference matters
Phys 133 -- Chapter 29 25
Electric potential two point charges
(from before)
Phys 133 -- Chapter 29 26
Point particle: potential representations
Phys 133 -- Chapter 29 27
Do Workbook 29.21
Phys 133 -- Chapter 29 28
Electric Potential: multiple charges
No vectors
Phys 133 -- Chapter 29 29
Do Workbook 29.25
Phys 133 -- Chapter 29 30
a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a.
Problem
b) Use the result for the dipole to find the electric potential at x=2 m, y=7 m when a=2 m, and Q=2 nC.
c) What is the potential energy of a proton placed there?
Phys 133 -- Chapter 29 31
Problem ans
r+ y-a
x
x
y+ar-
Phys 133 -- Chapter 29 32
Problem plot
Phys 133 -- Chapter 29 33
Problem ans
c) What is the potential energy of a proton placed there?
b) Use the result for the dipole to find the electric potential at x=7 m, y=2 m when a=2 m, and Q=2 nC.
Phys 133 -- Chapter 29 34
Potential of continuous charge distribution
where
Then let
solve
Phys 133 -- Chapter 29 35
The figure shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.
Problem 29.69
Phys 133 -- Chapter 29 36
Problem 29.69
x
y
P (d,0)
ri
ith
xi
d
Find potential at P due to ith bit of charge
Sum up contribution from each charge at P