General Physics 2 Electric Potential 1

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• Ve is the electrostatic potential energy relative to some

reference point• Volt: 1 V = 1 J/C

€

φ=Ve

q=

kQ

rPC

General Physics 2 Electric Potential 2

Analogy to Gravitational PE

Φb ΦaΦab

Electric potential energy depends on charge

Gravitation PE depends on mass

General Physics 2 Electric Potential 3

Electric Potential of Point Charge

• Set V=0 at a distance of infinity

General Physics 2 Electric Potential 4

Electric Potential of Multiple Charged Objects

• Superposition principle

€

φ=φ1 + φ2 + φ3 + ...+ φN

€

φ=kq1

rP1

+kq2

rP 2

+kq3

rP 3

+ ...+kqN

rPN

=kqi

rPii=1

N

∑

General Physics 2 Electric Potential 5

Electric Potential

General Physics 2 Electric Potential 6

Equipotential Lines

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

electric field lines

General Physics 2 Electric Potential 7

Electric Field & Equipotential Lines

• Draw field lines and equipotential lines for the following charge distributions

-

General Physics 2 Electric Potential 8

Electric Field & Equipotential Lines

• Draw field lines and equipotential lines for the following charge distributions

+

General Physics 2 Electric Potential 9

Relating Electric Field to Potential• The change in electrical potential for a

small displacement in a static electric field

€

dφ = −r E ⋅d

r r

€

E x, y,z( ) =

Ex x, y,z( )

Ey x, y,z( )

E z x, y,z( )

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥=

−∂φ ∂x

−∂φ ∂y

−∂φ ∂z

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

General Physics 2 Electric Potential 10

Electrostatic Potential & PE• When dealing with discrete point charges:

Ve and Φ are scalars F and E are vectors€

Ve =kq1q2

r

€

φ=kq

r

Electric Potential

+ charges move from high to low

potential

Think of analogy withgravitational PE, whereobject with positive PE willfall if released.

Here, p+ has high PE when near + plate and will“fall” toward negative platewhen released

Think of + charge whenwondering if something is high or low potential

Electric Potential

- charges move from low to high

potential

Unlike mass, charge canbe + or -. Thus, PE dependson the sign of the charge.

For example, an e- will havehigh PE when near the- plate and will “fall” toward the + plate when released

--High PElow PE

General Physics 2 Capacitors 13

Capacitance

• a capacitor stores electric charge

General Physics 2 Capacitors 14

Properties of Capacitors

• Capacitance, C• Q = C V• Farad (F) = Coulomb / Volt

• C depends on size, shape, relative position of parallel plates (and material that separates them)

permittivity offree space = 8.85 x 10-12 C2/(N m2)

surface areaper plate

separationbetween plates

General Physics 2 Electric Potential 16

Electron Volt, a Unit of Energy

• electron volt (eV)• Joule is very large for dealing w/electrons, atoms

and molecules• eV is energy required to move 1 e- through a

potential difference of 1V

• 1 eV = qe V = (1.6 x 10-19 C)(1.0 V)

1 eV = 1.6 x 10-19 J

General Physics 2 Electric Potential 17

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 PEExample:

- -

- +

ConcepTest

1. positive

2. negative

3. zero

ConcepTest

General Physics 2 Electric Potential 20

Plug & Chug

• How much work does the electric field do in moving a -7.7 C charge from the ground to a point whose potential is +55 V higher?

General Physics 2 Electric Potential 21

Think-Pair-Share

• How much kinetic energy will an electron gain (in joules and eV) if it accelerates through a potential difference of 23,000 V in a TV picture tube? What is its final velocity?

General Physics 2 Electric Potential 22

Electric Potential & Electric Field

• For a uniform electric field

uniform electricfield

General Physics 2 Electric Potential 23

Electric Field & Equipotential Lines

• Draw field lines and equipotential lines for the following charge distributions

- -

Which set has a positive potential energy?

Which set has a negative potential energy?

General Physics 2 Electric Potential 26

Plug & Chug

• What is the electric potential 15.0 cm from a 4.00 x 10-6 C point charge?

General Physics 2 Electric Potential 27

Think-Pair-Share

• What is the potential at point A, taking V=0 at a great distance?