Basic Terms
If you are looking for Electric Field and you know the Electric Potential
The product of two vectors in three dimensions
Cross Product
a region around a charged particle or object within which a force would be exerted on other charged particles or objects.
If you are looking for Charge Density and you know the Electric Potential
∇2 * Electric Potential = -(Charge Density/e0)
The product of the magnitude of each vector.
Dot Product
What should mirror image look like?
Mirror Image: point charge 'B' with charge '-q' at height 'h' below S
A way to describe the position of point A using variables[x,y,z]
Cartesian Coordinates
If you are looking for Charge Density and you know the Electric Field
∇ * Electric Field = Charge Density / e0
(dT/dx)i + (dT/dy)j + (dT/dz)k
∇ T
surface integral[E*ds] = Qenc / e0
a) Charge distribution
b) Electric Potential
c) Electric Field
A way to describe the vector at point A using variables[r,θ,ϕ]
Spherical Coordinates
If you are looking for Electric Potential and you know the Electric field
(Electric Potential at r - Electric Potential at r0) = -integral(Electric Field*dl) from r0 to r
A way to mathematically describe the difference between two vector functions
Divergence
If you have two surfaces, S1 & S2, with a point charge A with charge q above S1 and to the right of S2
what will the other images be
1. a point charge A1 with charge -q below S1 and to the right of S2
2. a point charge A2 with charge -q above S1 and to the left of S2
3. a point charge A3 with charge q below S1 and to the left of S2
A way to describe the relation between electric fields and electric potential
Gradient
If you are looking for Electric Potential and you know the Charge Density
A way to mathematically describe the rotating vectors
Curl
2. Spherical
3. Cyclindrical
Electric Potential = (q/4*pi*e0)*[(1/abs(r-rA))-(1/abs(r-rA1))-(1/abs(r-rA2))]