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# Today5/2 - PowerPoint PPT Presentation

Today5/2. Questions? E-Fields and Potential Difference (review). = k(2q o )/( 2 r o ) 2. E = kQ s /r 2. Many Charge Example. What is the force on +4q o ? (direction also). +q o. +4q o. Find the field at +4q o due to the “other” charges. These are the “source” charges. r o.

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• Questions?

• E-Fields and Potential Difference (review)

= k(2qo)/(2ro)2

E = kQs /r2

Many Charge Example

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

+qo

+4qo

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

ro

E+q = kQs/r2

= k(qo)/(ro)2

= Eo

-2qo

-3qo

Direction?

Away from + so right

E-2q = kQs/r2

= k2qo/2(ro)2

= k(qo)/(ro)2

= Eo

E-3q = kQs/r2

= k(3qo)/(ro)2

= 3kqo/(ro)2

= 3Eo

Etotal = 3.72 + 0.292 Eo

E = kQs /r2

Many Charge Example

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

+qo

+4qo

E+q = Eo

E-2q = Eo

E-3q = 3Eo

ro

Now add E-Field vectors

-2qo

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

-3qo

Ex = Eo - Eosin45

Ey = E-2q,y + E-3q,y

Ex = 0.29Eo

Ey = Eosin45 + 3Eo

 = tan-1(0.29/3.7) = 4.5°

Ey = 3.7Eo

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

= 3.71Eo

Fon +4q = 14.84kqo2/ro2 same direction as Etotal

1 larger

3 larger

2x

Stays the same

“Potential Energy Difference” and “Potential Difference”

Potential Energy DifferencePEA,Bis the change in PE the particularcharge feels when it is moved from one location to another.

Potential DifferenceVA,B is the change in PE a positive 1C charge would feelifit were moved from one location to another.

VA,B = +108 Volts, and q = +1C

VA,B = -108 Volts, and q = +1C

PEA,B = +100J

PEA,B = -100J

E field Difference”

Remember:From A to B!!!

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

E field

Which way does the E Field point?

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

VA,B = 108 Volts

Higher Potential

A

B

Higher Potential

VA,B = -108 Volts

E Fields point “downhill” with respect to potential difference

At which location is the potential highest? Difference”

At 2 downhill to 1 and 3

At which location is the potential lowest?

At 3 uphill to 1 and 2

Energy stored Difference”

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

Energy stored is the same as the work required to assemble the charges.

3m

4m

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

5m

(-) Difference”

Enet = 0

Enet = 0

How big is E?

(+)

W Difference”AB = qED

FHq

FE = qE

WAB = qED

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

A

B

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

PEAB = qED

PEAB = qDVAB

DVAB = EDAB