DESCRIPTION:
A physics music video deriving Gauss's Law using vector calculus. Written and performed by Lynda Williams, The Physics Chanteuse. Lyrics adapted from the Jackson E&M text. In Gaussian units. This is the first of 6 songs on Maxwell's equations. Music Mix by Lynda Williams.

Lyrics:

Equation One: Gauss'Law for the Electric Field
The flux of the E Field through a closed surface
(The integral of E dot ds)
Is due to the charge density contained inside
(4 pi integral of rho dV)
Put it all together, it reads:
(Surface integral of E is equal to
4 pi volume integral of rho dV)
Recall the divergence theorem for a vector A
(Closed surface integral of A is equal to the volume
integral of the divergence of A)
and apply it to Gauss' Law for E
(The surface integral of E is equal to the volume
integral of the divergence of E which is equal to 4
pi volume integral of rho dV)
Since the integrals are equal for any volume the
integrands are equal too, giving us the differential
form of the Law:
(del dot E is 4 pi rho)
Say it! (del dot E is 4 pi rho)
repetez! (del dot E is 4 pi rho)
one more time! (del dot E is 4 pi rho)
What does it mean?
The flux of the E field though a closed surface is
due to the charge density contained inside!
Electric charges produce electric fields!
Maxwell's Equations! Our salvation!
Maxwell's equations are 4 mathematical equations that relate the Electric Field (E) and
magnetic field (B) to the charge (ρ ) and current (J) densities that specify the fields and give rise to electromagnetic radiation - light.