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Physics Equations: E&M


AlphaGeek

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Part 2 of the equation posts: E&M. Again, if you see any mistakes or have a few equations to add, make sure to utilize the comment section! I'll add it in right away.

Electrostatics

png.latex?F_e=\frac{kq_1q_2}{r^{2}}

E= Fe/q = kq/r

λ = Q/L

ρ = Q/V

σ = Q/A

Electric potential

Ue = kq1q2/r

F = -dU/dl

V = k ∑ qi/ri = W/q

∆V= Vb - Va = ab E dl = ∆U/q

Gauss's Law:

png.latex?$$\int\limits_{closed surface}

Conductors

Esurface= png.latex? \frac{\sigma}{\epsilon_{0} }

Vinside = png.latex? \frac{Q}{4\pi \epsilon _{0}R}

Einside = png.latex? 0

Capacitor

C=Q/V = png.latex? \frac{\epsilon _{0} A}{d}

Uc =png.latex? \frac{1}{2}CV^{2}

Ue = field energy density = png.latex? \frac{U}{volume}

Energy = V/d

C= png.latex? \frac{\kappa \epsilon _{0}A } w/ png.latex? \kappa = Dielectric constant

Circuits

I = png.latex? \frac{\Delta Q}{\Delta t}

I = V/R

I = NqVdA = NeVdA

Current density (J) = NqVd = I/A

charging up: w = I2V

charging down: U = png.latex? \frac{1}{2} CV2

png.latex? \tau = RC

5 png.latex? \tau = 99% charged/discharged

Resistance

R= png.latex?\frac{\rho L}{A}

E= png.latex?\frac{V}{L}

P=IV

E= png.latex? \rho J

W= qv

Series Circuit

Ceq = png.latex? \frac{Q}{V}

png.latex? \frac{1}{C_{eq}} = \frac{1}{C

I= constant

V=IR

Req= R1+R2+...

Q=CV

Parallel Circuit

Ceq = C1 + C2 + ...

I = V/R

V= constant

png.latex? \frac{1}{R_{eq}} = \frac{1}{R

Q=CV

Batteries:

Videal = png.latex? \Delta V = png.latex? \varepsilonmf = VT

V with resistance = png.latex? \varepsilon Iri = VT

Pbattery = W/t = png.latex? \frac{\Delta \varepsilon}{t}= Ipng.latex?\varepsilon

Pexternal resistor = I2R

Pinternal resistor = I2ri

Magnetism

Gauss's Law: png.latex? \phi = \oint B \cdot dA = O

Amphere's Law: png.latex? \oint B \cdot dl = \mu_{0} Ipen

...for a wire of radius R, B = png.latex? \frac{\mu_{0} I }{2 \pi R^{2}

Biot-Savart law: dB = png.latex? \frac{\mu_{0} I}{4 \pi r^{2}} (dl X r)

...for a loop of wire, B = png.latex? \frac{\mu_{0} I}{2r}

Faraday's Law: png.latex? \varepsilon = \frac{d \phi_{B

= png.latex?\frac{-d}{dt} \oint_{open surf

= png.latex? \int E \cdot dl

solenoid: B = png.latex? \frac{mu_{0} I N}{L}

toroid: B = png.latex? \frac{mu_{0} I N}{2 \pi r}

Mag. moment (png.latex?\mu) =NIA =NIpng.latex?\piR2

Mag. torque= png.latex?\mu_{0} X B = \mu_{0} B sin\th

...sorry that took so long to post up, jeez that code takes a while to type up ^-^ Feel free to add/correct in the comments section!

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