Coulomb’s Lawand Electric Fields

Recall Coulomb’s Law

• Magnitude of the force between charges q1 and q2 separated a distance r:

F = k q1q2/r2 k = 9x109 Nm2/C2

• Force on nucleus of Hydrogen from e-

F = (9x109)(1.6x10-19)(1.6x10-19)/(10-10)2 N

= 2.3x10-8 N (to the right)

+ -

r = 1x10-10 m

Qp=1.6x10-19 C Qe = -1.6x10-19 CF

5

Electric Field• Charged particles create electric fields.

– Direction is the same as for the force that a + charge would feel at that location.

– Magnitude given by: E F/q = kq/r2

+

r = 1x10-10 m

Qp=1.6x10-19 C

E

E = (9109)(1.610-19)/(10-10)2 N = 1.41011 N/C (to the right)

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What is the direction of the electric field at point B?

1) Left

2) Right

3) Zero

x

yA

B

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Since charges have equal magnitude, and point B is closer to the negative charge net electric field is to the left

E FieldWhat is the direction of the electric field at point C?

1) Left

2) Right

3) Zero

x

y

C

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Away from positive charge (right)

Towards negative charge (right)

Net E field is to right.

Red is negative

Blue is positive

Comparison:Electric Force vs. Electric Field

• Electric Force (F) - the actual force felt by a charge at some location.

• Electric Field (E) - found for a location only – tells what the electric force would be if a charge were located there:

F = Eq• Both are vectors, with magnitude and direction.

Add x & y components. Direction determines sign.

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What is the direction of the electric field at point A?

1) Up

2) Down

3) Left

4) Right

5) Zerox

yA

B

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Red is negative

Blue is positive

E Field IIWhat is the direction of the electric field at point A, if

the two positive charges have equal magnitude?

1) Up

2) Down

3) Right

4) Left

5) Zero

x

yA

B

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Red is negative

Blue is positive

Electric Field Lines• Closeness of lines shows

field strength- lines never cross

• # lines at surface Q

• Arrow gives direction of E- Start on +, end on -

42

A B

X

Y

Charge A is

1) positive 2) negative 3) unknown

Field lines start on positive charge, end on negative.

44

A B

X

Y

Compare the ratio of charges QA/ QB

1) QA= 0.5QB 2) QA= QB 3) QA= 2 QB

# lines proportional to Q

45

A B

X

Y

The magnitude of the electric field at point X is greater than at point Y

1) True 2) False Density of field lines gives E

46

The electric field is stronger when the lines are located closer to one another.

E Field Lines

Compare the magnitude of the electric field at point A and B

1) EA>EB 2) EA=EB 3) EA<EB

A

B

47

E inside of conductor• Conductor electrons free to move

– Electrons feels electric force - will move until they feel no more force (F=0)

– F=Eq: if F=0 then E=0

• E=0 inside a conductor (Always!)

48

A B

X

Y

"Charge A" is actually a small, charged metal ball (a conductor). The magnitude of the electric field inside the ball is:

(1) Negative (2) Zero (3) Positive

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Recap• E Field has magnitude and direction:

– EF/q

– Calculate just like Coulomb’s law

– Careful when adding vectors

• Electric Field Lines– Density gives strength (# proportional to charge.)

– Arrow gives direction (Start + end on -)

• Conductors– Electrons free to move E=0