Fields and Fluids Flashcards by Noah Fenton

Q

Volume integral in spherical coordinates

A

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Q

Total charge of a configuration

A

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Q

Electric field of a configuration

A

Choose a Gaussian surface
Then use Gauss’ law in integral form:

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Q

Coulomb’s law

A

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Q

Area of a sphere

A

4𝜋𝑟^2

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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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Q

Properties of Tensors

A

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Q

Decomposition of rank-2 tensors

A

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Q

Decomposition of a symmetric tensor

A

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Q

Transformation rule of a rank-2 tensor

A

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Q

Tensor components

A

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Q

Symmetry of 𝜀 and 𝛿

A

𝜀 - anti-symmetric
𝛿 - symmetric

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Q

Vorticity

A

𝜔 = ∇ × 𝑞

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Q

Circulation

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

A

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Q

Stream functions

A

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Q

Constant streamline equations

A

Q

Complex velocity

A

Q

Wave equations in a vacuum

A

Q

Plane wave equations

A

Q

Electrostatics equations

A

Q

Magnetostatics equations

A

Q

Gauss’ law in integral form

A

Q

Ampère’s law in integral form

A

Q

Electromotive force

A

Electric flux through a sphere

Rotation matrix, about the z-axis

Reflection matrix in a line L through the origin

Stagnation points of a system

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

Electric flux of a point charge

Polar coordinates

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

Matrix product in index notation

Acceleration

Compressibility

A fluid is incompressible if the rate of change of its density is zero: `D𝜌/Dt`