# Chapter 28 Electric Potential Phys 133 – Chapter 30.

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Chapter 28 Electric Potential Phys 133 – Chapter 30

Looking ahead New force (Chapter 25) New potential energy (Chapter 28)
Phys Chapter 29

Electric Potential Energy (Uelec)
Gravitational Uniform electric field Point charge Phys Chapter 29

Gravitational potential (energy)
Defined Then defined For the gravitational force Wgrav=(-mg)(∆y)=mg(yi-yf) ∆Ugrav=-Wgrav=mg(yf-yi) In general Phys Chapter 29

Uniform field: Electric potential energy
where Phys Chapter 29

Uniform field: Electric potential energy
Direction of lower potential energy depends on type of charge Positive charge Negative charge Lower potential energy Lower potential energy s s Phys Chapter 29

Do Workbook 29.6 Phys Chapter 29

Problem 29.3 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) Phys Chapter 29

Electrical Potential Energy of Two Point Charges
where Phys Chapter 29

Question 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? 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? Phys Chapter 29

Question ans Like charges Opposite charges Phys Chapter 29

Do Workbook 29.3 Phys Chapter 29

Problem 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 Phys Chapter 29

Problem ans Phys Chapter 29

Electric Potential (Velec)
Gravitational Uniform electric field Point charge Phys Chapter 29

Electric Potential (Velec)
Charge creates potential define Potential only depends on source charges Look at Gravitational Uniform electric field Point charge Phys Chapter 29

Gravitational Potential
object environment Environment only Phys Chapter 29

Electric potential capacitor
s (from before) object environment Environment only Phys Chapter 29

Capacitor: potential representations
Phys Chapter 29

Draw V(x) for the two equipotential surfaces
Draw U(x) for a proton in these potentials Draw U(x) for an electron in these potentials Phys Chapter 29

Workbook 29.18b extension A 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 Chapter 29

Workbook 29.18b extension ans
electron proton Not enough energy to reach a Phys Chapter 29

Problem Modified In the figure which capacitor plate, left or right, is the positive plate? What is the electric potential energy of a proton at the midpoint of the capacitor? What is the electric field strength inside the capacitor? In general What is the electric field strength inside the capacitor in terms of  and o? What is the electric field strength inside the capacitor in terms of ∆V and d (the distance between the plates? Phys Chapter 29

Only potential difference matters
Phys Chapter 29

Electric potential two point charges
(from before) Phys Chapter 29

Point particle: potential representations
Phys Chapter 29

Do Workbook 29.21 Phys Chapter 29

Electric Potential: multiple charges
No vectors Phys Chapter 29

Do Workbook 29.25 Phys Chapter 29

Problem a) Find an expression for the electric potential V(x,y) for a dipole with point charges +/- Q at y= +/- a. 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 Chapter 29

Problem ans r+ y+a y-a r- x x Phys Chapter 29

Problem plot Phys Chapter 29

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. c) What is the potential energy of a proton placed there? Phys Chapter 29

Potential of continuous charge distribution
where Then let solve Phys Chapter 29

Problem 29.69 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. Phys Chapter 29

Problem 29.69 d ith P (d,0) xi ri y x
Sum up contribution from each charge at P x y d ith P (d,0) xi ri Find potential at P due to ith bit of charge Phys Chapter 29