Formulario di Fisica 2

Formulario completo di Elettromagnetismo: elettrostatica, magnetismo, induzione, onde EM, ottica, fisica moderna. Tutte le formule in PDF.

Electrostatic Field and Potential
Electric Charges and Coulomb's Law
F=14πε0∣q1q2∣r2F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{|q_1 q_2|}{r^2}
e=1.602×10−19 Ce = 1.602\times10^{-19}\,\mathrm{C}
ε0=8.85×10−12 C2/(N⋅m2)\varepsilon_0 = 8.85\times10^{-12}\,\mathrm{C^2/(N\cdot m^2)}
Electric Field
E⃗=14πε0qr2r^\vec{E} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\hat{r}
Ewire=λ/(2πε0r),Eplane=σ/(2ε0)E_{wire} = \lambda/(2\pi\varepsilon_0 r),\quad E_{plane} = \sigma/(2\varepsilon_0)
Electric Potential
V=q4πε0rV = \dfrac{q}{4\pi\varepsilon_0 r}
E⃗=−∇V\vec{E} = -\nabla V
Vdip=pcos⁡θ4πε0r2V_{dip} = \dfrac{p\cos\theta}{4\pi\varepsilon_0 r^2}
Gauss's Law
∮SE⃗⋅dA⃗=Qint/ε0\oint_S\vec{E}\cdot d\vec{A} = Q_{int}/\varepsilon_0
∇⋅E⃗=ρ/ε0\nabla\cdot\vec{E} = \rho/\varepsilon_0
∇2V=−ρ/ε0(Poisson)\nabla^2 V = -\rho/\varepsilon_0 \quad (\text{Poisson})
Conductors in Equilibrium and Electrostatic Energy
C=Q/V,Cplate=ε0A/dC = Q/V,\quad C_{plate} = \varepsilon_0 A/d
U=CV2/2=Q2/(2C)U = CV^2/2 = Q^2/(2C)
u=ε0E2/2u = \varepsilon_0 E^2/2
Dielectrics
D⃗=ε0εrE⃗\vec{D} = \varepsilon_0\varepsilon_r\vec{E}
∇⋅D⃗=ρfree\nabla\cdot\vec{D} = \rho_{free}
Cdiel=εrC0C_{diel} = \varepsilon_r C_0
Magnetic Field and Electric Currents
Electric Current and Ohm's Law
I=dq/dt  [A],J⃗=σE⃗I = dq/dt\;[\mathrm{A}],\quad \vec{J} = \sigma\vec{E}
R=ρL/A,V=RIR = \rho L/A,\quad V = RI
P=I2R=V2/R(Joule)P = I^2R = V^2/R \quad (\text{Joule})
Magnetic Force on Charges and Conductors
F⃗=qv⃗×B⃗\vec{F} = q\vec{v}\times\vec{B}
dF⃗=I dl⃗×B⃗d\vec{F} = I\,d\vec{l}\times\vec{B}
r=mv/(qB),ωc=qB/mr = mv/(qB),\quad \omega_c = qB/m
Sources of Magnetic Field — Biot-Savart Law
dB⃗=μ04πI dl⃗×r^r2d\vec{B} = \dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec{l}\times\hat{r}}{r^2}
Bwire=μ0I/(2πr),Bsol=μ0nIB_{wire} = \mu_0 I/(2\pi r),\quad B_{sol} = \mu_0 nI
Ampère's Law and Vector Potential
∮CB⃗⋅dl⃗=μ0Ienc\oint_C\vec{B}\cdot d\vec{l} = \mu_0 I_{enc}
∇×B⃗=μ0J⃗,∇⋅B⃗=0\nabla\times\vec{B} = \mu_0\vec{J},\quad \nabla\cdot\vec{B} = 0
B⃗=∇×A⃗\vec{B} = \nabla\times\vec{A}
Magnetic Materials
H⃗=B⃗/μ0−M⃗\vec{H} = \vec{B}/\mu_0 - \vec{M}
B⃗=μ0μrH⃗\vec{B} = \mu_0\mu_r\vec{H}
∇×H⃗=J⃗free\nabla\times\vec{H} = \vec{J}_{free}
Electromagnetic Induction and Maxwell's Equations
Faraday's Law and Induced EMF
E=−dΦB/dt\mathcal{E} = -d\Phi_B/dt
∇×E⃗=−∂B⃗/∂t\nabla\times\vec{E} = -\partial\vec{B}/\partial t
ΦB=∫SB⃗⋅dA⃗\Phi_B = \int_S\vec{B}\cdot d\vec{A}
Self-Inductance and Magnetic Energy
EL=−L dI/dt\mathcal{E}_L = -L\,dI/dt
UL=LI2/2,uB=B2/(2μ0)U_L = LI^2/2,\quad u_B = B^2/(2\mu_0)
Lsol=μ0n2VL_{sol} = \mu_0 n^2 V
Displacement Current and Maxwell's Equations
∇⋅E⃗=ρ/ε0,∇⋅B⃗=0\nabla\cdot\vec{E}=\rho/\varepsilon_0,\quad \nabla\cdot\vec{B}=0
∇×E⃗=−∂B⃗/∂t,∇×B⃗=μ0J⃗+μ0ε0∂E⃗/∂t\nabla\times\vec{E}=-\partial\vec{B}/\partial t,\quad \nabla\times\vec{B}=\mu_0\vec{J}+\mu_0\varepsilon_0\partial\vec{E}/\partial t
c=1/μ0ε0c = 1/\sqrt{\mu_0\varepsilon_0}
RLC Circuits and AC Currents
ω0=1/LC\omega_0 = 1/\sqrt{LC}
Z=R2+(XL−XC)2Z = \sqrt{R^2+(X_L-X_C)^2}
P=VrmsIrmscos⁡ϕP = V_{rms}I_{rms}\cos\phi
Electromagnetic Waves
Plane Electromagnetic Waves in Vacuum
c=1/μ0ε0=2.998×108 m/sc = 1/\sqrt{\mu_0\varepsilon_0} = 2.998\times10^8\,\mathrm{m/s}
E⃗⊥B⃗⊥k⃗,∣E∣=c∣B∣\vec{E}\perp\vec{B}\perp\vec{k},\quad |E|=c|B|
ω=ck,k=2π/λ\omega = ck,\quad k = 2\pi/\lambda
Polarization, Energy, and Momentum
S⃗=1μ0E⃗×B⃗\vec{S} = \dfrac{1}{\mu_0}\vec{E}\times\vec{B}
I=⟨S⟩=cε0E022I = \langle S\rangle = \dfrac{c\varepsilon_0 E_0^2}{2}
Prad=I/c  (absorption)P_{rad} = I/c\;(\text{absorption})
Propagation in Media and Reflection
n=c/v=εrμrn = c/v = \sqrt{\varepsilon_r\mu_r}
n1sin⁡θi=n2sin⁡θt(Snell)n_1\sin\theta_i = n_2\sin\theta_t \quad (\text{Snell})
sin⁡θc=n2/n1(critical angle)\sin\theta_c = n_2/n_1 \quad (\text{critical angle})
Electromagnetic Spectrum and Waves in Conductors
c=λf=2.998×108 m/sc = \lambda f = 2.998\times10^8\,\mathrm{m/s}
δ=2μ0σω(skin depth)\delta = \sqrt{\dfrac{2}{\mu_0\sigma\omega}} \quad (\text{skin depth})
Optics — Interference, Diffraction, and Geometric Optics
Interference — Young's Double Slit
Δr=mλ⇒maximum\Delta r = m\lambda \Rightarrow \text{maximum}
ym=mλL/d(Young)y_m = m\lambda L/d \quad (\text{Young})
Δfilm=2nt±λ/2\Delta_{film} = 2nt \pm \lambda/2
Fraunhofer Diffraction
I=I0(sin⁡α/α)2,α=πasin⁡θ/λI = I_0(\sin\alpha/\alpha)^2,\quad \alpha=\pi a\sin\theta/\lambda
asin⁡θ=mλ(minima)a\sin\theta = m\lambda \quad (\text{minima})
θmin=1.22λ/D(Rayleigh)\theta_{min} = 1.22\lambda/D \quad (\text{Rayleigh})
Diffraction Grating
dsin⁡θ=mλ(maxima)d\sin\theta = m\lambda \quad (\text{maxima})
R=mN\mathcal{R} = mN
2dsin⁡θ=mλ(Bragg)2d\sin\theta = m\lambda \quad (\text{Bragg})
Geometric Optics — Mirrors and Lenses
1/p+1/q=1/f=2/R(mirror)1/p + 1/q = 1/f = 2/R \quad (\text{mirror})
1/f=(n−1)(1/R1−1/R2)(lensmaker)1/f=(n-1)(1/R_1-1/R_2) \quad (\text{lensmaker})
m=−q/p(magnification)m = -q/p \quad (\text{magnification})
Modern Physics — Quantum and Solid State
Thermal Radiation and Planck's Hypothesis
P=σT4A,σ=5.67×10−8 W/(m2K4)P = \sigma T^4 A,\quad \sigma=5.67\times10^{-8}\,\mathrm{W/(m^2K^4)}
λmaxT=2.898×10−3 m⋅K\lambda_{max}T = 2.898\times10^{-3}\,\mathrm{m\cdot K}
E=hν=hc/λE = h\nu = hc/\lambda
Photoelectric Effect and Compton Scattering
KEmax=hν−ϕKE_{max} = h\nu - \phi
Δλ=λC(1−cos⁡θ)\Delta\lambda = \lambda_C(1-\cos\theta)
Eph=hν,pph=h/λE_{ph}=h\nu,\quad p_{ph}=h/\lambda
Wave-Particle Duality and Heisenberg Uncertainty
λ=h/p(de Broglie)\lambda = h/p \quad (\text{de Broglie})
Δx⋅Δp≥ℏ/2\Delta x\cdot\Delta p \geq \hbar/2
ℏ=h/(2π)\hbar = h/(2\pi)
Bohr Model and Energy Levels
En=−13.6 eV/n2E_n = -13.6\,\mathrm{eV}/n^2
hν=Eni−Enfh\nu = E_{n_i} - E_{n_f}
1/λ=RH(1/nf2−1/ni2)1/\lambda = R_H(1/n_f^2 - 1/n_i^2)
Energy Bands and Semiconductors
Eg(Si)=1.1 eV,Eg(Ge)=0.67 eVE_g(Si)=1.1\,\mathrm{eV},\quad E_g(Ge)=0.67\,\mathrm{eV}
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