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Chapter 18: Electric Charges, Forces, and Fields

Brent Royuk Phys-112

Concordia University

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Electric Charge •  Electrostatics vs. Electricity •  Historical Development

–  Elektron and Magnesia

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Electric Charge Basics •  Like repels, opposites attract •  Charge can move •  Two kinds of charge

–  How do you know it’s only two? •  Two materials: insulators and conductors •  Neutral means balanced charge

–  So a water stream is always attracted: polarization •  Charge by contact or induction

–  Charging by induction: which charge does it get? –  What is an electrical ground?

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Electric Charge Basics •  Charge by contact or induction

–  Charging by induction: which charge does it get? –  Simulation

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Charging by Induction

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Electric Charge •  Franklin’s single fluid model, 1747

–  surplus (glass) or deficiency (rubber/amber) –  Unfortunate coin toss

•  Actually, we know it’s electrons that move: surplus = –, deficiency = +. –  And electron is negative, proton is positive. Bummer.

•  Triboelectric Charging (charging by rubbing) •  Metric unit of charge: the Coulomb (a lot of charge)

–  1 Coulomb = 6.25 x 1018 electrons –  Usually more useful: charge of electron –  e = 1.6 x 10-19 C

•  Notice inverse relationship •  Classical electromagnetism does not require the use of

electrons •  Charge symbol, q, and q = ne (charge is quantized) •  Van de Graaf & Wimshurst •  Franklin’s Kite

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Big Sparks

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Coulomb’s Law •  The inverse square relationship

–  Just like gravity

•  The Law

–  k = 9.0 x 109 Nm2/C2 –  More fundamental:

•  εo = 8.85 x 10-12 C2/N m2

€

F =kq1q2

r2

€

k =1

4πεo

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Coulomb’s Law Examples •  What is the Coulomb force between two 1C

charges one meter apart? From here to Lincoln?

•  What is the Coulomb force between two protons separated by r = 1 x 10-15 m?

•  Example 18.1: •  •  If two +1.0 µ charges experience a force of

0.23 N, how far apart must they be?

€

FE

FG

= 2.27 x 1039

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The Electric Field •  To circumvent the idea of

instantaneously propagating forces we posit the existence of a force field

•  We call this the electric field, E –  E is a vector. –  Handwritten notation:

•  A field is a quantity that has a value at every point in space. –  For example, a temperature map is a scalar

field and a windspeed map is a vector field

•  And guess what: Fields are real!

€

! E

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The Electric Field •  Definition:

–  Direction is defined by how a positive “test charge” qo would move

•  For a point charge,

•  Note the difference between q and qo

€

! E =

! F qo

€

E =Fqo

=

kqqo

r 2

qo

=kqr 2

+q

What is here?

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Electric Vector Fields •  Vectors can be found for any point near

the charge configuration •  This defines the electric field

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The Electric Field •  Examples

–  What is the electric field vector 12 cm away from a point charge of -42 µC?

–  An isolated electron is acted on by an electric force of 3.2 x 10-14 N. What is the magnitude of the electric field at the electron’s location?

–  A 3.2 ng dust particle contains an excess of a billion electrons. What is the direction and magnitude of an E-field that would keep the particle from falling?

–  Two charges of +4.0 µC and +9.0 µC are 30 cm apart. Where on the line joining the charges is the electric field zero?

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Electric Field Lines •  Replace vector arrows with continuous

lines. –  The field is always in the direction of the

lines. –  Direction defined by positive test charge. –  Note that more lines/area means a

stronger field –  Can field lines cross?

•  Examples –  Single point Charge –  Like and unlike point charge pairs

•  Dipoles •  See next page

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Electric Field Lines

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The Parallel-Plate Capacitor •  A Capacitor stores

charge •  Between parallel

plates the E-field is quite uniform.

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Charges on a Conductor 1.  The electric field is zero everywhere inside a charged

conductor –  If it were not, the charges would re-arrange themselves

until it is 2.  Any excess charge on an isolated conductor resides

entirely on the surface of the conductor –  Since charges repel each other and are free to move in a

conductor 3.  The electric field at the outer surface of a charged

conductor is perpendicular to the surface.

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Charges on a Conductor 4.  The excess charge on a

conductor in electrostatic equilibrium is more concentrated at regions of greater curvature. –  Again, tangential

components would move charges

–  Therefore the E-field is concentrated at tips of conductors

–  The lightning rod

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The Faraday Cage •  Movie •  What is the safest place to hide during a lightning storm?