Electricity

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Electricity

• Charge and Field

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Static Electricity

• Comb picks up paper
• Balloon sticks to wall
• Sparks when combing hair
• Shock when touch doorknob
• static cling in dryer
• lightning

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Two Kinds of Charge

• Unlike charges attract
• Like charges repel
• Positive on rubbed glass rod
• Negative on rubbed plastic rod

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Conservation of Charge

• Net amount of electric charge produced in any
  process is zero
• When positive and negative combine they
  neutralize
• Most every day objects are neutral
• Ordinary atoms are neutral

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Atoms Contain Charge

• Protons inside nucleus are positive
• Electrons outside nucleus are negative
• Charge on proton same as on electron
• Electrons can move within solid material

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Methods of Charging

• Rubbing
• Induction
• Separates charge
• Contact
• Grounding
• Connect with wire
• leading to ground

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Charging by Induction
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Insulators and Conductors

• Conductors carry charge easily
• Metals have many free electrons
• Ionic liquids
• Plasmas
• Insulators conduct poorly
• Dry gases, pure molecular liquids
• Wood, paper, cloth, glass, etc
• Semiconductors like silicon, germanium

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Electroscope

• Detects charge with leaves that repel
• or rotating needle

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Coulombs Law

• Electric force proportional to product of charges
  divided by square of distance between them
• Q in coulombs
• k is Coulomb constant
• k 8.988x109 Nm2/C2
• constant e0 is permittivity
• of free space 8.85x10-12 C2/Nm2
• Applies to point charges

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Electrostatic force vs. gravity force

• FE kq1q2/r2 k 9 x 109 Nm2/C2
• FG Gm1m2/r2 G 6.67 x 10-11 Nm2/kg2
• Electrostatic force both attractive and repulsive
• Gravitational force only attractive (per Newton,
  not so certain today)

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The Smallest Charge

• Charge on electron or elementary charge qe or e
• e 1.602 x 10-19 Coulombs
• Charge is quantized
• Discrete amounts only
• 1e, 2e, 3e, 4e etc
• Quarks of sub-atomic physics have 1/3 and 2/3
  charge

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Example Calculate Coulomb Force

• Find the force between two objects with charge 1
  Coulomb at a separation of one meter
• F kq1q2/r2 9 x 109 x 1/1 9 x 109 N
• If objects are 100Kg students, what will be
  initial acceleration?
• a F/m 9 x 107 m/s/s
• Estimate speed reached in one second

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Example(2) Coulomb Force

• Find force between two 1 micro (10-6) coulomb
  charges at separation of 20 cm
• F kq1q2/r2 9 x 109x 10-6 x 10-6 /(0.20)2
• 9/(.04) x 10-3

2.25 x 10 -1 N
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Electrostatic Force and Vectors

• Fnet F1 F2 F3
• Called principle of superposition of forces
• Use component method of vector addition
• Fx F1x F2x Fy F1y F2y

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Component Method Review

• F1X F1cosq
• F1Y F1sinq
• FX F1XF2X
• FY F1YF2Y
• F (FX2 FY2)1/2
• TanQ FY/FX

F1
F1Y
q
F1X
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Three Charges in a Line

Assuming the magnitude of all three charges is
equal, what is the direction of the net force on
the positive charge?
To the right
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Three Charges in a Line

Assuming the magnitude of all three charges is
equal, what is the direction of the net force on
the red positive charge?
To the right
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Three Charges in a Line

Assuming the magnitude of all three charges is
equal, what is the direction of the net force on
the red positive charge?
To the left
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Electric Field kq/r2

• Force acting at a distance vs. field concept
• Field E is force on tiny positive test charge
  divided by magnitude of charge
• Direction same as force on charge
• Field line spacing shows strength of E

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Electric field lines outward from charge
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Electric field lines inward to - charge
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Field due to 2 Like Charges
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Field due to Unlike Charges
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You Predict

• What would be the direction of the force on a
  positively charged pith ball near a positively
  charged Van de Graaf sphere?
• What about a negatively charged pith ball?
• If the force on a positively charged pith ball is
  toward the sphere, what must be the field
  direction?
• What is the charge on the sphere?

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Electric Field Strength

• Units newtons per coulomb
• E F/q F Eq q is test charge
• E kQ/r2 due to charge Q

Just Coulombs law without the q2
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Problem Solving

• Draw careful diagram
• Apply Coulombs Law to get magnitude of forces or
  fields
• Determine direction of net forces by considering
  like and unlike charges
• Show and label each vector force or field
• Add vectorially to get resultant
• Use symmetry when possible

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Fields and Conductors

• Field inside conductor is zero(static)
• If not force FqE would make charges move
• Charge spreads out maximally on surface
• Charge Q inside spherical uncharged shell induces
  Q on inside surface of shell
• Positive charge Q exists on outside
• Electric field just outside a conductor is always
  perpendicular to the surface

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Why Field Outside Conductor is Perpendicular to
Surface

• Ask what if there were a parallel component just
  outside
• There would also be one just inside
• Electrons would move until equilibrium
• Then there could be no field
• Contradiction
• Therefore the original statement is true

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Problem

• Charged conducting spheres with 3Q and Q are
  initially at a distance of L meters apart. They
  are brought together briefly, then moved back to
  their original positions. What happens to the
  force between them?

-Q
3Q
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Problem

• Charged conducting spheres with 3Q and Q are
  initially at a distance of L meters apart. They
  are brought together briefly, then moved back to
  their original positions. What happens to the
  force between them?

-Q
3Q
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Problem

• Charged conducting spheres with 3Q and Q are
  initially at a distance of L meters apart. They
  are brought together briefly, then moved back to
  their original positions. What happens to the
  force between them?

Q
Q
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Problem

• Charged conducting spheres with 3Q and Q are
  initially at a distance of L meters apart. They
  are brought together briefly, then moved back to
  their original positions. What happens to the
  force between them?

Q
Q
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Solution

• On contact there is neutralization leaving a
  total of 2Q each charge gets Q. Upon putting
  the charges back where they were, the force
  changes from attractive to repulsive and is 1/3
  as strong.

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Question

• What would happen if a positive charge is placed
  at the center of a neutral conducting spherical
  shell?

Draw the electric field lines
Negative charges induced, inside shell, positive
outside as shown on NEXT SLIDE
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