mit8_02sc_lectureslides08

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Module 08: Electric Potentialand Gausss Law; Configuration

Energy

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Module 08: Outline

Usin Gausss Law to find V from EConfiguration Energy

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E Field and Potential: Creatin

A point charge qcreates a field and potential around it:r

2;E r

e ek V k

r r

= = se superpos on orsystems of charges

They are related:

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;E E sB AA

V V V V d= = r

rr


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= =

If you put a charged particle, (charge q), in a field:

=

r r, ,

and the particle does not change its kinetic energyen:

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ext


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Derivin E from V

E sB

V d = r

r

A

r

A = x,y,z , B= x+x,y,z

s x=( , , )

E s

x x y z

V d

+

=

r

r

E s

r

r ( )

E ixx E x= =

r

V V E = Rate of chan e in V

( , , )x y z

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x x x with y and z held constant


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Derivin E from VIf we do all coordinates:

E i + j k

V V V = +

r

x y z

E V= r

+x y z= +

Gradient (del) operator: i j + k

x z +

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E from V

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Demonstration:Making & Measuring

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Two Concept QuestionQuestions:

o en a e

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Concept Question: E from V

The above shows potential V(x). Which is true?

1. Ex > 0 is > 0 and Ex < 0 is > 0

. x > 0 x < 03. Ex > 0 is < 0 and Ex < 0 is < 0

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4. Ex > 0 is < 0 and Ex < 0 is > 05. I dont know


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Potential from E

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E=

r r2

0

,4

r a r br

< b No field160

V r V=

123 0 dr= 0= No change in V!


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Potential for Nested Shells

Region 2: a < r< b

= drQr

( ) ( )V r V r b = 0r

0=14243

r

= 40r

r=b

=1

Q

1

1

0

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Electric potential is DIFFERENT surroundings matter


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Potential for Nested Shells

Region 3: r< a

= dr0

a

r

=0( ) ( )V r V r a =

14 431 1kQ

a b

=

V r( )= V a( )= Q 1 1 r0

=

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Confi uration Ener

How much energy to put two charges as pictured?

1 First char e is free2) Second charge sees first:

1 q q 12

=2

= q2 1

=4 r

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= =

Confi uration Ener

How much energy to put three charges as pictured?

1) Know how to do first two

r ng n r :

q3

q1

q2

3 3 1 2

40 r13 r23

Total configuration energy:

U = W2

+ W3

=1 q

1q

2 +q

1q

3 +q

2q

3 = U12 + U13 + U23

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0 12 13 23


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Problem: Build It

1) How much energy

did it take to assemblethe charges at left?

2) How much energy

would it take to add ath +

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MIT OpenCourseWarehttp://ocw.mit.edu

8.02SC Physics II: Electricity and Magnetism

Fall 2010

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