Physics > Solutions Guide > Rutgers University - PHYSICS 750:227Formula Sheet (All)

Rutgers University - PHYSICS 750:227Formula Sheet

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Formula Sheet Electromagnetic Waves Electric field and Magnetic field form sinusoidial relationships expressed such as sin ⁡(kx+ωt) E (t )=Emax¿ ; B (t )=Bmax(sin (kx+ωt )) Where k is the wa ... ve number, and ω is the angular frequency Maxwell’s Equations tells us that E=cB ; B=ϵ 0 μ0CE ; c= 1 √ϵ0 μ0 c being the speed of light, μ0 being the permitivvity of free space (4pi * 10^-7 These waves have a wavelength λ , velocity v, and frequency, which are expressed in the fluid relationship; f = ω 2 π ; v=(2 2ωkπ π)=λf = 2kπ2∗πϖ ; We should also know the following potential energy densities produced by both fields, as well as the totals U E= 12 ϵ 0 E2 ; U B= 12 B2 μ0 ; U tot=U E+U B ; U tot=2U E=2UB AS well as the relationships of the average energy densities, and the root-mean-squares. U Eave= 12 ϵ 0(√E20)2 ; UBave=21μ0(√B20)2 ; Erms=√E20 ; Brms=√B20 ; And the peculiar Poyntig, S, which is known as the intensity of the wave. S= E0 B0 2 μ0 = E0 2 c ϵ0 2 = B0 2 c 2 μ0 And the definitions of power P=ϵ 0 c E2=ϵ0 c2 EB= EB μ0 And energy stored per unit volume ϖ= ϵ0 E2 2 + B2 2 μ0 = ϵ0 E2 2 + E2 2 μ0 c2= ϵ0 E2 2 + ϵ0 E2 2 =ϵ 0 E2 Pressure, Intensity, and their relation with Electric field didn’t show up in the Masteringphysics example, but it’s in a former final, so I have no idea if this is relevant, but just in case . [Show More]

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