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Physics 202, Lecture 2

Today’s Topics

Electric Fields (Ch 21.6-21.11) Determining the Electric Field of given charge

distribution (discrete and continuous) Electric Field Lines Motion of Charged Particles in External Electric Fields

Announcements: No honors lecture tomorrow

Coulomb’s Law: Vector Form

!F21= ke

q1q2

r2r̂ = !

!F12

2 charges: force on q2 by q1

12r̂

principle of linear superposition

Multiple charges: force on charge i

F12

F21

F12

F21

Examples (board): 21.18, 21.20

!Fi =

!Fij

j

! = kqiqj

rij2r̂ij

i

!

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The Electric Field

Original (Coulomb’s) view: q applies electric force on q0 (action at a distance)

Force on charge always proportionalto strength of that charge!

“Modern” view:q is source of electric field E, which fills all of space.

Interaction with the field leads to a force on q0

!F = k

q0q

r2r̂

!F = q

0kq

r2r̂ = q

0

!E q: source charge

E independent of q0!

q0

qF

F

(q0 often called the “test charge”: take the limit as )q0! 0

Aside: Vector and Scalar Fields

What is a field?

A physical quantity which has a value at each pointin space (for example: temperature, wind speed,…)

Here we will consider only scalar fields (e.g., temperature, electricpotential,…) and vector fields (e.g., windspeed, electric fields,…)

Concept of the electric field (and the magnetic field) is the most useful way to describe the physics of electromagnetism.

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A Scalar Field

77 82

83685566

8375 809091

757180

72

84

73

8288

92

7788

887364

These isolated temperatures sample the scalar field(you only learn the temperature at the point you choose,

but T is defined everywhere (x, y)

A Vector Field

7782

83685566

8375 809091

757180

72

84

73

57

8892

77

5688

7364

This is a vector field(specify both wind speed and direction)

Example: the way the wind is blowing…

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Calculating the Electric Field for aGiven Charge Distribution

E field of point charge q:

Multiple point charge sources

Continuous distributions:

!E = k

q

r2r̂

!E =

!Ei

i

! = kqi

ri2r̂i

i

!

d!E = k

dq

r2r̂

!r

q

P

(observation point)

!E = d

!E!

!r

dq

P

Examples: 21.41, 21.40 (ring), line charge, disk

Visualizing the Electric Field: Field Lines

+

+ chg

Field lines

Visualize the electric field of a positive point charge:

Magnitude: local density of linesDirection: direction of arrows

Rules for Field Lines:

Field lines start or end only on charges (never empty space). They start on positive and end on negative charges.

Field lines of point charges extend toinfinity (true for any localized distributionwith nonzero net charge).

Field lines can never cross.

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Example: Point-Like Charges

+q -q

!E(!r ) = k

q

r2r̂

!E(!r ) = k

q

r2r̂

Examples: Two Charged Particles

+q and +q +q and -q(dipole)

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Two Charged Particles

Motion Of Charged Particle In Uniform Electric Field

Fundamental Formulas:

F=qE

a=F/m = qE/m v= vi +at

E

+q

-q

If initially at rest (vi =0) then v= at = (qE/m) t

Motion of +q:Same dir. as E

Motion of - q:

Opposite dir. as E

Examples: 21.56, 2d example (next slide)

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Exercise: An Electron in a Uniform E. Field

Find out vertical displacement after the electronpasses through a downward uniform electric field E

Answer: y= - ½ (e/m)E (l/vi)2