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PHYS 1022: Chap. 27, Pg 2

Topics: •  Electric fields from point charges •  Electric fields from continuous distributions •  Motion in electric fields

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PHYS 1022: Chap. 27, Pg 3 New Topic

PHYS 1022: Chap. 27, Pg 4

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PHYS 1022: Chap. 27, Pg 5

PHYS 1022: Chap. 27, Pg 6

€

Fg =G Mr2m = mg

M m

Q q

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PHYS 1022: Chap. 27, Pg 7

1.  E1 > E2

2.  E1 = E2

3.  E1 < E2

PHYS 1022: Chap. 27, Pg 8

1.  E1 > E2

2.  E1 = E2

3.  E1 < E2

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PHYS 1022: Chap. 27, Pg 9

  Assume the point is x away from the +4Q charge to the right.

3R

-Q +4Q x

Discard x=-2R solution because it’s unphysical.

PHYS 1022: Chap. 27, Pg 10

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PHYS 1022: Chap. 27, Pg 11

PHYS 1022: Chap. 27, Pg 12

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PHYS 1022: Chap. 27, Pg 13

PHYS 1022: Chap. 27, Pg 14

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PHYS 1022: Chap. 27, Pg 15

1 m θ

100 nC + +

100 nC

1 m

PHYS 1022: Chap. 27, Pg 16 New Topic

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PHYS 1022: Chap. 27, Pg 17

  Divide charge into small chunks   Treat each chunk as a point charge

  Superposition principles of electric fields.   Add up contribution from all chunks   Sum becomes integral

(vector sum)

. P

What’s electric field at point P due to the charge distribution?

dq

r

PHYS 1022: Chap. 27, Pg 18

  How do we represent the charge “Q” on an extended object?

total charge Q

small pieces of charge

dq

  Surface of charge:

σ = charge per unit area

dq = σ dA

  Line of charge:

λ = charge per unit length

dq = λ dx

  Volume of charge:

ρ = charge per unit volume

dq = ρ dV

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PHYS 1022: Chap. 27, Pg 19

1.  1/2 2.  3/2

3.  1/3 4.  4/9 5.  4/3

PHYS 1022: Chap. 27, Pg 20

Which arrow best represents the electric field at a point on the middle line from a positive line

charge?

P 1

2

3

4

1)  1 2)  2 3)  3 4)  4 5)  None of

these

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PHYS 1022: Chap. 27, Pg 21

Which of the following actions will increase the electric field strength at the position of the dot?

1)  Make the rod longer without changing the charge. 2)  Make the rod fatter without changing the charge. 3)  Make the rod shorter without changing the charge. 4)  Remove charge from the rod. 5)  Make the rod narrower without changing the charge.

PHYS 1022: Chap. 27, Pg 22

+ + + + + + + + + + + + + + + + +

L

R

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PHYS 1022: Chap. 27, Pg 23

+ + + + + + + + + + + + + + + + + x = -L/2

R x = L/2 x = 0

r x

as R >> L, we see that the denominator becomes R2,

and so the electric field becomes:

which is just the electric field of a point charge!

PHYS 1022: Chap. 27, Pg 24

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PHYS 1022: Chap. 27, Pg 25

The figure shows a uniformly charged positive wire. Five small, equally-spaced segments of charge are shown. • Use these five segments to estimate the wire’s electric field—both magnitude and direction—at each point in space marked with a dot. Draw each electric field on the figure. • Redraw the rod and fields, replacing the + changes on the left half with - charges

PHYS 1022: Chap. 27, Pg 26

+

+

+

+

+

+

+

+

+

+

+

+

+ + +

Hint: a small piece of arc length ds on a circle of radius R is given by:

ds = R dθ

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PHYS 1022: Chap. 27, Pg 27

  A ring of radius a carries a total charge Q distributed uniformly around it. Determine the electric field at a point on its axis.

PHYS 1022: Chap. 27, Pg 28

  Break up the charge into small pieces, then add up the fields from each piece as a vector sum. (use charge density dQ=λ dl)

  Use symmetry to simplify the problem.

  Check special cases where you know or expect the answer. If it doesn’t check out, the result would be wrong entirely.

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PHYS 1022: Chap. 27, Pg 29

  A ring of radius a carries a total charge Q distributed uniformly around it. Determine the electric field at a point on its axis.

By symmetry: Ey=0 So E is along x-axis.

Set up coordinate system:

PHYS 1022: Chap. 27, Pg 30

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PHYS 1022: Chap. 27, Pg 31

PHYS 1022: Chap. 27, Pg 32 New Topic

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PHYS 1022: Chap. 27, Pg 33

PHYS 1022: Chap. 27, Pg 34