Fields and Fluids Flashcards

1
Q

Volume integral in spherical coordinates

A
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2
Q

Total charge of a configuration

A
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3
Q

Electric field of a configuration

A

Choose a Gaussian surface
Then use Gaussโ€™ law in integral form:

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4
Q

Coulombโ€™s law

A
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5
Q

Area of a sphere

A

4๐œ‹๐‘Ÿ^2

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6
Q

Finding components of curl and divergence

A
  • Divergence (.) is already its own component
  • Curl (x) need to take its i-th component
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7
Q

Properties of Tensors

A
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8
Q

Decomposition of rank-2 tensors

A
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9
Q

Decomposition of a symmetric tensor

A
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10
Q

Transformation rule of a rank-2 tensor

A
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11
Q

Tensor components

A
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12
Q

Symmetry of ๐œ€ and ๐›ฟ

A

๐œ€ - anti-symmetric
๐›ฟ - symmetric

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13
Q

Vorticity

A

๐œ” = โˆ‡ ร— ๐‘ž

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14
Q

Circulation

and the circulation around a circle, centre origin, radius r

A
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15
Q

Stream functions

A
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16
Q

Constant streamline equations

A
17
Q

Complex velocity

A
18
Q

Wave equations in a vacuum

A
19
Q

Plane wave equations

A
20
Q

Electrostatics equations

A
21
Q

Magnetostatics equations

A
22
Q

Gaussโ€™ law in integral form

A
23
Q

Ampรจreโ€™s law in integral form

A
24
Q

Electromotive force

A
25
Q

Electric flux through a sphere

A
26
Q

Rotation matrix, about the z-axis

A
27
Q

Reflection matrix in a line L through the origin

A
28
Q

Stagnation points of a system

A

Points of vanishing velocity, where:
for q(u,v), u = v = 0

29
Q

Electric flux of a point charge

A
30
Q

Polar coordinates

A

r^2 = x^2 + y^2
x = r cos(theta)
y = r sin(theta)

31
Q

Matrix product in index notation

A
32
Q

Acceleration

A
33
Q

Compressibility

A

A fluid is incompressible if the rate of change of its density is zero: D๐œŒ/Dt