Electric vs. Gravitational

Potential Energy

• Work is needed to push an object against gravity and give it Potential Energy

Gravitational Potential Energy Increases

g

• Work is needed to push a charge against a field and give it Electric Potential Energy

Electric Potential Energy Increases

E

+-

∆Ug = m g h ∆Ue = q E d

Potential Energy & Potential Difference

Potential Difference

Voltage (scalar or vector)

What does voltage actually measure?– Measures how much

energy a charge will gain/lose

– Measures how much work that can be done by a charge

Divide both sides by q and you get another physical quantity: Electric Potential! Otherwise known as voltage!

If the Electric Field is constant, V = Ed

∆Ug = Ed q

V = ∆Ug = Ed q If the Electric Field is not

constant, then you plug the equation in for E, ie. for a point charge.

V = Ed (kQ/r2)d = kQ/r

Uniform

Electric Fields

Allesandro Volta(Italian: 1745 – 1827)Parallel Plates

Point charge

Uniform electric field

Note the field lines

Potential Energy & Potential D

ifference

–2–

LowPotential Energy

- - - - - - - - -

+++++++++E

HighPotential Energy

LowPotential Energy

HigherPotential Energy

Why does this one have more potential

energy?

Potential Energy & Potential D

ifference

2+

- - - - - - - - -

+++++++++E

High or Low PE?

High or Low PE?

A change in PE means …

Potential Energy & Potential D

ifference

–2–

- - - - - - - - -

+++++++++E

Which of these has greater electrical potential

energy per charge?

more ELECTRIC POTENTIAL ENERGY

Same ELECTRIC POTENTIAL

Potential Energy & Potential D

ifference

–2–

- - - - - - - - -

+++++++++E

Which of these has experienced a greater

change in electrical potential energy?

Which of these has experienced a greater change in electrical potential energy per charge?

Analogy

12 V0 V

Battery gives the electron 12 J of Potential energy

e “loses” energy as it travels through the circuit.

Battery “gives” energy back to electron to repeat cycle

Potential Energy & Potential D

ifference

• Sample ProblemThe electric field is 625 N/C between 2 large charged parallel plates are 4 cm apart.a. What is the electric potential difference

between the plates? b. What work will you do to move a proton

from the – to the + plate?+ + +

–––

D = 0.04mp+

a) V = E d = (625N/C)(0.04m) = 25 V

E = 625 N/Cd = 0.04 mq = 1.6 x 10-19 C

b) W = Ue = q ∆V = (25 V)(1.6 x 10-19C) Ue = 4.0 x 10-18 J

Key Ideas

Electric Force

Electric Potential Energy

Electric Potential,Potential,Voltage

Electric Fields

Symbol F Ue V E

Defin- ition

Push or pull on a charge

Total Potential Energy

Energy per charge Area around a charge that affects other charges.

Derivation

Energy per distance or Field x charge

Force x Distance or Field x charge

Energy per charge or Field x distance

Force per charge or Voltage per distance

Unit Newtons (N)

Joules(J)

Volts(V or J/C)

Newtons/Coulomb (N/C) Volts/Meter (V/m)

Equation F = kQq/r2

F=E qUe= kQq/r = -qEd = qV

ΔV = ΔU/qV=-Ed

E=kQ/r2

E=-V/d

Flow C

hartcom

pliments of M

ike Gearon

times charge

per unit charge

times distance = Work

per unit distance

= Potential Gradient