chapter 18: electric charges, forces, and fields1 chapter 18: electric charges, forces, and fields...
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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?
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