Physik 1b Formeln

\(\vec F = {1\over4 \pi \epsilon_0} {q_1q_2 \over r^2}{\vec r \over r}\)

mit \(\epsilon_0 = 8,85*10^{-12} \; C^2N^{-1}m^{-2} \)

\(\vec E( \vec r) = {1 \over 4\pi \epsilon_0} {Q\over r^2}{\vec r \over r}\)

\(\vec E(\vec r) = {1\over 4\pi \epsilon_0}{Q_i \over |\vec r-\vec {r_i}|^2}{\vec r-\vec {r_i}\over |\vec r-\vec {r_i}|}\)

\(\vec E(\vec r) = {1\over 4\pi \epsilon_0} \int {dQ \over |\vec r-\vec r'|^2}{\vec r-\vec r'\over |\vec r-\vec r'|}\)

\(\vec p = q*2\vec a\)

\(E_{pot }= q{1 \over 4 \pi \epsilon_0}{Q\over r}\) ... potentielle Energie

\(U(r) = \displaystyle\sum_i{Q_i \over 4\pi \epsilon_0}{1 \over |\vec r-\vec r_i|}\) ... elektrisches Potential [1 eV]

\(1\ eV = 1,602*10^{-19}J\)

\(x(t)=x_0*cos(\omega t+\varphi)\)

\(x_0 ... Amplitude\)

\(\omega ... Kreisfrequenz\)

\(\varphi ... Phasenwinkel\)

Fallunterscheidung:

Federpendel:      \(\omega = \sqrt{k_F \over m}\)

Schwerependel: \(\omega = \sqrt{g \over l}\)

physikalisches Pendel:  \(\omega = \sqrt{mgl \over I}\)

komplexe Zahl ... \(z=x+iy\)

Polarkoordinaten:

\(r=\sqrt{x^2+y^2}\)

\(\varphi = arctan({y \over x})\)

\(x = r*cos(\varphi)\)

\(y = r*sin(\varphi)\)

Polardarstellung einer komplexen Zahl ... \(z = r*(cos(\varphi)+i*sin(\varphi))=r*e^{i \varphi}\)

\(z=z_1*z_2=r_1*r_2*(cos(\varphi_1+\varphi_2)+i*sin(\varphi_1+\varphi_2))\)

\(e^{ix} = cos(x) + i*sin(x)\)