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17 Cards in this Set
- Front
- Back
Divergence of a gradient
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Laplacian
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Curl of a gradient
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= 0
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Gradient of Divergence
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Seldom occurs. Not the same as Laplacian of a vector
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Divergence of a Curl
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= 0
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Curl of a Curl
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Fundamental Theorem for Gradients
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(Ignore the P)
- Independent of the path taken from a to b - Closed integral = 0 |
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Fundamental Theorem for Divergences
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aka "Gauss's Theorem, Green's Theorem, or Divergence Theorem"
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Fundamental Theorem for Curls
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"Stokes Theorem"
- the cross part depends only on the boundary line, not on the particular surface used. - closed integral for cross part equals zero for any closed surface |
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An example of a 3D Dirac-Delta Function
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Helmholtz Theorem
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Any field can be uniquely determined by it's divergence and curl and knowing it's boundary conditions
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Irrotational (Curl-less) Fields Theorem
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Solenoidal (Divergence-less) Fields Theorem
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Coulomb's Law of Electric Fields
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Gauss's Law
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Electric Potential
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Poisson's Equation
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The Triangle Diagram based on the three fundamental quantities of electrostatics
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