1. Scalars, Vectors and Fields
In mathematical physics, the quantities can be in scalar or vector form.
Scalar quantities: speed, temperature, pressure (measure of force experienced by collision from
surroundings), electrostatic potential or voltage (measure of local electrical potential energy).
Vector quantities: velocity, acceleration, angular momentum(how quickly a mass is rotating about
an axis) and electric field (force experienced by electric charge due to neighboring charges)
Field can be describe in Cartesion, Cylindrical or Spherical coordiantes.
2. Cartesian Coordiantes
3. Coordinates Systems Convert
3. Contour Integrals
3. Vector Addition
4. Vector Subtraction
5. Vector Multiplication
𝐴𝑦𝐵𝑧 − 𝐴𝑧𝐵𝑦
𝐴𝑥
𝐵𝑥
𝐴 = [𝐴𝑦] 𝐵 = [𝐵𝑦] ∴ 𝐴 × 𝐵 = [ 𝐴𝑧𝐵𝑥 − 𝐴𝑥𝐵𝑧 ]
𝐴𝑥𝐵𝑦 − 𝐴𝑦𝐵𝑥
𝐵𝑧
𝐴𝑧
In cross product when calculating each axis term, ignore those terms from each vector and do
cross multiply and minus them, top left one (y) will be postive, for y specifically it will be negative.
6. Electric charge, Field and Flux
The 𝜖̅ represents electric field, and it can generate a Force exerting on each other given its
charge.
7. Sources – Electric Charge
8. Coulomb’s Law
The experiment derived law Coulomb said the magnitude of electrostatic force
experienced by one of two charges in a pair of charges is given by the expression
above.
9. Vector Coulomb’s Law
10. Multiple Charges
11. Electric Field Lines
12. Charge Distributions