EM Part 1 - 1 Flashcards
Part 1.1 - What is divergence?
It is how much field lines converge or diverge at a point.
In a 2D field, a negative divergence means convergence and a positive divergence means divergence.
What is curl?
How much field lines curve or curl (e.g. laminar or turbulent flow).
What is the gradient of scalar field?
What is the equation for a 3D field? m
The gradient is a vector that points in the direction of maximum change in slope and the magnitude of that vector is equal to the rate of change in that direction.
What is the integral mathematical expression for Guass’s law for the electric field?
And explain the components.
The expression states that for a source of a field within an enclosed surface Ω, then the total flux that crosses the surface will correspond to the flux emanating from the source.
This is represented by taking the integral of the dot product between D (electric flux density) and dΩ (a very small area) over the enclosed surface area of Ω.
What is Flux?
The variation of a field( described by the field lines) as a flux flowing through space.
What is the mathmetical expression for the total charge in a volume?
Were rho is the charge density.
What is the divergence of a field defined as?
The divergence is a measure of the total flux emanating from each point in space, essentially a measure of the strength of the point as a source for the field.
What is Gauss’s Therorem / Divergence Theorem ?
Why is Guass’s Theorem useful?
It is useful as it allows you to convert an integral over a volume into an integral over its boundary (the surface that encloses it).
So the theorem shows is that the sum of the vector fields over the surface leads to the same value as finding the divergence of the vector field lines across the volume.
The same logic could be applied to the electric flux density.
What is the divergence of the electric flux density given as in a region of volume charge density ρ?
Definition of curl?
What is the full expression for curl in cartesian coordinates?
What is Stokes’ Theorem?
Stokes’ Theorem relates the surface integral of the curl of a vector field to the line integral of the same vector field around the boundary of the surface.
What is Lorentz’s Force Equation?
where q is a charge
Guass’s Law for the Magnetic Field?
Gauss’s law for a magnetic field states that the total/net magnetic flux coming out of volume enclosed by a surface S is zero.
What do we get when we apply Gauss’s Theorem (Divergence Theorem) to a magnetic field?
What is the conservation of charge continuity condition and what is the resultant equation if Guass’s Theorem (Divergence Theorem is applied) ?
What is the formal definition of faraday’s law and what is corresponding equation?
If C is a closed curve that forms the boundary to a surface Ω, “The time-rate of change of the total magnetic flux through Ω is equal to the negative of the total e.m.f. measured around C.”
What is the resulting equation if Stoke’s Theorem is applied to Faraday’s Law?
What does this symbol represent?
Current Density
What is Ampere’s – Maxwell Law in integral and differential form respecitvely?
Define each of the variables.
H - magnetic field intensity
- J* - conduction current
- dD/dt -* displacement current
What are the boundary conditions that can be derived from Faradays law on an long infinitmismal loop?
What are the bounday conditions of Ampere’s Law for a long infitimismal loop?
What are the E and H boundary conditions for long infinitesimal loop that is a perfect conductor?
Considering this coin shaped volume,
What is faradays law in integral and differential form?
What are the constitutive relations that you need to know?
What is the differential form of gauss’s law for the electric field?
