Today5/2

Questions? E-Fields and Potential Difference

(review)

Many Charge ExampleE = kQs /r2

+qo

-3qo

+4qo

-2qo

ro

What is the force on +4qo? (direction also)

Find the field at +4qo due to the “other” charges. These are the “source” charges.

E+q = kQs/r2 = k(qo)/(ro)2 = Eo

Direction? Away from + so right

E-2q = kQs/r2 = k(2qo)/(2ro)2 = Eo= k2qo/2(ro)2= k(qo)/(ro)2

E-3q = kQs/r2 = k(3qo)/(ro)2 = 3Eo= 3kqo/(ro)2

Many Charge ExampleE = kQs /r2

+qo

-3qo

+4qo

-2qo

ro

What is the force on +4qo? (direction also)

E+q = Eo E-2q = Eo E-3q = 3Eo

Now add E-Field vectors

Ex = E+q,x + E-2q,x

Ex = Eo - Eosin45

Ex = 0.29Eo Ey = E-2q,y + E-3q,y

Ey = Eosin45 + 3Eo

Ey = 3.7Eo

= tan-1(0.29/3.7) = 4.5°

Etotal = 3.72 + 0.292 Eo = 3.71Eo

Fon +4q = (4qo)3.71Eo = 14.84qoEo

Fon +4q = 14.84kqo2/ro

2

same direction as Etotal

What direction would the force point on a small positive charge at 1,2,3?

Compare the size of the force exerted on a small charge at

a. 1 and 2b. 2 and 3

The test charge is doubled when at 2

a. how does the force change?b. how does the electric field change?

2x

Stays the same

3 larger1 larger

“Potential Energy Difference” and “Potential Difference”

Potential Energy Difference PEA,B is the change in PE the particular charge feels when it is moved from one location to another.Potential Difference VA,B is the change in PE a positive 1C charge would feel if it were moved from one location to another.

VA,B = +108 Volts, and q = +1CPEA,B = +100J

VA,B = -108 Volts, and q = +1CPEA,B = -100J

Which way does the E Field point?

PEA,B = +100J, and q = +1C What is VA,B?

VA,B = 108 Volts

VA,B = -108 Volts

PEA,B = +100J, and q = -1C What is VA,B?

A B

Higher Potential

Higher Potential

E Fields point “downhill” with respect to potential difference

E field

E field

Remember:From A to B!!!

At which location is the potential highest?

At 2 downhill to 1 and 3

At which location is the potential lowest?

At 3 uphill to 1 and 2

How much energy is stored in the assembly of charges? All are +1 x 10-3C and 1g (1 x 10-3kg).

4m

5m

3mEnergy stored is the same as the work required to assemble the charges.

Move them all very far away, bring them in one at a time, and total up the work done.

Energy stored r

kQV

0

V

VqPE

(+)

How big is E?(-)

Enet = 0

02E

02

E 0

netE

Enet = 0

B A

What is the change in potential energy in going from A to B?

FE = qEFHq

WAB = qED

PEAB = qED

PEAB = qVAB

VAB = EDAB

WAB = qED

Only applies when the field is uniform over the distance. VAB‘s sign depends on the direction of E. In this case it’s positive.