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General Physics 2 Electric Potential 2

Electric Potential

• As with mechanics, energy is a useful quantity in

studying electric forces

• electric potential or potential
  • electric potential energy per unit charge
• potential difference, Φ
  • only difference in potential energy is meaningful
  • V e is the electrostatic potential energy relative to some reference point
  • Volt : 1 V = 1 J/C " = V

e

q

kQ r

PC

General Physics 2 Electric Potential 4 Electric Potential of Point Charge

• Set V=0 at a distance of infinity

General Physics 2 Electric Potential 5

Electric Potential of Multiple Charged Objects

• Superposition principle

N

kq

1

r

P 1

kq

2

r

P 2

kq

3

r

P 3

kq

N

r

PN

kq

i

r

i = 1 Pi N

General Physics 2 Electric Potential 7

Think-Pair-Share

• What is the potential at point A, taking V=0 at

a great distance?

General Physics 2 Electric Potential 8

Electric Potential

General Physics 2 Electric Potential 10

Equipotential Lines

• connect points in space at same potential
• equipotential surface is perpendicular to

electric field lines

General Physics 2 Electric Potential 11

Relating Electric Field to Potential

• The change in electrical potential for a small displacement in a static electric field ! d " = # r E $ d r r E (^) ( x , y , z ) = E x ( x ,^ y , z ) E y ( x ,^ y , z ) E z ( x ,^ y , z ) "

$ $ $ % & ' ' ' = ( )* ) x ( )* ) y ( )* ) z "

$ $ $ % & ' ' '

Electric Potential

• charges move from high to low potential Think of analogy with gravitational PE, where object with positive PE will fall if released. Here, p+ has high PE when near + plate and will “fall” toward negative plate when released Think of + charge when wondering if something is high or low potential

Electric Potential

• charges move from low to high potential Unlike mass, charge can be + or -. Thus, PE depends on the sign of the charge. For example, an e- will have high PE when near the
• plate and will “fall” toward the + plate when released

low PE High PE

General Physics 2 Electric Potential 16

Sign of Electric PE

• PE = 0 at infinity
• Did you have to do work to bring charges from

infinity?

• yes -> charges have positive PE Example:
• no -> charges have negative PE Example:

Which set has a positive potential energy?

ConcepTest

General Physics 2 Capacitors 20

Capacitance

• a capacitor stores electric charge