Fields and Fluids Flashcards
Volume integral in spherical coordinates
Total charge of a configuration
Electric field of a configuration
Choose a Gaussian surface
Then use Gaussβ law in integral form:
Coulombβs law
Area of a sphere
4ππ^2
Finding components of curl and divergence
- Divergence (.) is already its own component
- Curl (x) need to take its i-th component
Properties of Tensors
Decomposition of rank-2 tensors
Decomposition of a symmetric tensor
Transformation rule of a rank-2 tensor
Tensor components
Symmetry of π and πΏ
π - anti-symmetric
πΏ - symmetric
Vorticity
π = β Γ π
Circulation
and the circulation around a circle, centre origin, radius r
Stream functions
Constant streamline equations
Complex velocity
Wave equations in a vacuum
Plane wave equations
Electrostatics equations
Magnetostatics equations
Gaussβ law in integral form
AmpΓ¨reβs law in integral form
Electromotive force
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: Dπ/Dt
