Reminder

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Reminder

• Mid term examination
• Tuesday after break
• 2nd Homework Sheet due the Thursday after.

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Mid -term

• 5 questions on paper
• Full Marks for 2 questions
• Much better to do full questions
• 1 question on mathematical methods
• 1 question on electrostatics
• 1 question on potential theory
• 2 questions on magnetostatics

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Mathematical Review
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Surface Integrals

• Surface integrals

Outward drawn normal
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The unit normal is required to be in the ve
direction

• If the surface is closed then the ve direction
  is taken to be out

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The fundamental Theorem for curls

• TheoremStokes

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• Electrostatics

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Coulombs Law
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Comments

• Using SI units
• ?0 is known as the permitivity of free space
• The vector r is the vector connecting the two
  points
• In general

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Concept of Field
Idea Space around electric charge is altered so
if we put Another charge in the neighborhood of
the first it will experience a force.
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Principle of Superposition
The interaction between any two charges is
completely unaffected by the presence of
others. Which means to find the total field at a
point we add the field due to all the charges
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Let us assume Gausss Law is true then consider
a point charge at the origin, construct a sphere
around q then clearly by symmetry the field must
be radial and we have
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Potential Theory
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Magnetostatics
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Steady Currents
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• Note a moving point charge can not constitute a
  steady current
• When a steady current flows in a wire, its
  magnitude,I,must be the same all along the wire,
  otherwise charge would be pilling up somewhere
  and ? would not be a constant in time

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• Stationary charges electrostatics
• Steady current magnetostatics

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Biot-Savart Law
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Biot-Savart Law

• Law only applies to steady currents
• It does not apply to moving point charges

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• Find the magnetic field a distances from a long
  straight wire carrying a steady current

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(1)
(2)
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where J is constained to be within the volume,W
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Ampères Law
Ampères Law
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• Hence

of Poissons
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• We have shown that there exists a solution A s.t.

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In cartesian coordinates
3 sets of Poissons equations
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• We may assume J goes to zero at infinity
• Then we can solve