{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Formula sheet

# Formula sheet - Formula Sheet J = E(Ohm's law d E = dt(flux...

This preview shows pages 1–2. Sign up to view the full content.

Formula Sheet ~ J = σ ~ E (Ohm’s law) E = - d dt Φ (flux rule) Φ = MI (self-inductance M) M 12 = μ 0 4 π H S 1 H S 2 d ~ l 1 · d ~ l 2 | ~ r 1 - ~ r 2 (mutual inductance) ∂t ρ = - ~ ∇ · ~ J (conservation laws) ∂t ( u mech + u em ) = - ~ ∇ · ~ S ∂t ( p mech + p em ) = ~ ∇· T ~ S = 1 μ 0 ~ E × ~ B (Poynting vector) T ij = 0 ( E i E j - 1 2 δ ij E 2 ) + 1 μ 0 ( B i B j - 1 2 δ ij B 2 ) (Maxwell’s stress tensor) ~ A 0 = ~ A + λ (Gauge transformation) V 0 = V - ∂t λ ~ ∇ · ~ A = 0 (Coulomb gauge) ~ ∇ · ~ A = - μ 0 0 ∂t V (Lorentz gauge) Λ μ ν = γ - γβ 0 0 - γβ γ 0 0 0 0 1 0 0 0 0 1 , β = v c , γ = 1 1 - β 2 (Lorentz transformation with boost in x-direction) g μν = g μν = - 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 (metric tensor) 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
F μν =
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern