ELECTROSTATICS

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ELECTROSTATICS
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Outline

• Electric Force, Electric fields
• Electric Flux and Gaub law
• Electric potential
• Capacitors and dielectric (Electric storage)

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The physics of charged objects

• Study of electricity aims to understand the
  interaction between different charged objects.

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The physics of charged objects

• Study of electricity aims to understand the
  interaction between different charged objects.

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Structure of Matter

• Fundamental building blocks of the matter are
  atoms.

- electrons
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neutral neutrons
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protons
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Structure of Matter

• Neutral atom electron Positive ion

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Structure of Matter

• Fundamental building blocks of the matter are
  atoms.

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Structure of Matter

• Neutral atom electron negative ion.

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ELECTRICALLY CHARGING OBJECTS

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neutral object
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ELECTRICALLY CHARGING OBJECTS

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positive object
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ELECTRICALLY CHARGING OBJECTS

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negative object
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Charging by Induction

• In metals outer atomic electrons are not bound to
  any atoms (electron see).

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Charging by Induction

• In metals outer atomic electrons are not bound to
  any atoms (electron see).

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Charging by Induction
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Electric Polarization

• Same atoms have weakly bound electrons.

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Electric Polarization

• Same atoms have weakly bound electrons.

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Electric Polarization
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The Electric Force
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Coulombs Law

• Quantifies the electric force between two charges.

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Coulombs Law

• Quantifies the electric force between two charges.

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Coulombs Law

• Quantifies the electric force between two charges.

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Electric Force Field

• Gravitational force field

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Electric Force Field
Q
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Electric Force Field
Q
q
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Electric Force Field

• Definition of Electric field

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Electric Force Field

• Definition of Electric field

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Electric Force Field





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Electric Force Field

• The electric field due to a number of source
  charges is given by the expression

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Electric Force Field
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Electric Force Field(Linear distribution of
charge)
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Electric Force Field(Linear distribution of
charge)
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Electric Force Field(Linear distribution of
charge)
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Electric Force Field(Surface distribution of
charge)
da
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Electric Force Field(Surface distribution of
charge)
da
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Electric Force Field(Surface distribution of
charge)
da
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Electric Dipole

• Electric dipole consists of a pair of point
  charges with equal size but opposite sign
  separated by a distance d.

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Electric Dipole

• Electric dipole consists of a pair of point
  charges with equal size but opposite sign
  separated by a distance d.

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Electric Dipole

• Electric dipole consists of a pair of point
  charges with equal size but opposite sign
  separated by a distance d.

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Electric Dipole

• Electric dipole consists of a pair of point
  charges with equal size but opposite sign
  separated by a distance d.

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Electric Dipole

• Water molecules are electric dipoles

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Exercise 1

• A point charge q -8.0 nC is located at the
  origin. Find the electric field vector at the
  point x 1.2 m, y -1.6 m

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Exercise 2

• An electric dipole consists of a positive charge
  q and negative charge q separated by a distance
  2a, as shown in the figure below. Find the
  electric field due to these charges along the
  axis at the point P, which is the distance y from
  the origin. Assume that ygtgta.

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q
q
y
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Vector Flux
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Vector Flux
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Vector Flux

• Definition of flux

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Electric Flux
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Electric Flux
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Gaubs Law
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Gaubs Law

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Gaubs Law

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Gaubs Law

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Gaubs Law

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Exercise 3
dE
R
L
s
r
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Solution

• Coulombs Law

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Solution

• Infinitesimal area of disk

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Solution

• Infinitesimal area of disk

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Solution

• Y-component of E-field element

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Solution
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Solution

• Y-component of E-field element

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Solution

• Y-component of E-field element

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Solution

• Y-component of E-field element

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Solution

• Y-component of E-field element

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Two Oppositely charged Parallel Plates (Capacitor)
s
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Two Oppositely charged Parallel Plates (Capacitor)
s
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Exercise 4
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Electric Potential
Charge with potential
Q
q
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Electric Potential
Source charge generates a potential at this
position
Q
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Electric Potential
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Electric Potential
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Electric Potential
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Electric Potential
Electric potential at position P due to a system
of N source charges is given by
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Electric Potential

• Potential difference

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Electric Potential

• Potential difference

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Electric Potential
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Two Oppositely charged Parallel Plates (Capacitor)
s
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V
-V
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Two Oppositely charged Parallel Plates (Capacitor)
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Capacitors and di-electrics

• Capacitors store electric potential energy

Battery

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Capacitors and di-electrics

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Capacitors and di-electrics
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Capacitors and di-electrics

• We can therefore express the voltage across the
  capacitor plates as follows

• Hence

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Exercise 3

• A parallel-plate capacitor has an area of A
  2 cm2 and a plate separation of d 1mm.
• Find its capacitance. (answer 1.77pF)
• If the plate separation of this capacitor is
  increased to 3 mm, find the capacitance. (answer
  0.59 pF).

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Capacitors and di-electrics

• Capacitors in Parallel

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Capacitors and di-electrics

• Di-electric material inside a parallel Electric
  field.

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Capacitors and di-electrics

• Di-electric material between parallel capacitor
  plates.

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Capacitors and di-electrics

• Di-electric material between parallel capacitor
  plates.

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Capacitors and di-electrics

• Di-electric material between parallel capacitor
  plates.

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Capacitors and di-electrics

• Di-electric material between parallel capacitor
  plates.

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Capacitors and di-electrics

• Di-electric material between parallel capacitor
  plates.