Electricity & Magnetism

EQUATIONS
   INFORMATION
$$ \large F_e = \frac{kq_1 q_2}{r^2} $$

\(\\ {F_e} = electrostatic \hspace{4 pt} force \hspace{4 pt} (N) \\ \textbf{k} = electrostatic \hspace{4 pt} constant \\ \hspace{5 pt} (8.988 \hspace{2 pt} x \hspace{2 pt} 10^9 \hspace{4 pt} N \hspace{2 pt} m^2 \hspace{4 pt} C^{-2}) \\ {q_{\#}} = charge \hspace{4 pt} \# \hspace{4 pt} (C)\\ \textbf{r} = distance \hspace{4 pt} between \hspace{4 pt} the \hspace{4 pt} charges (m)\)
 
$$ \large E = \frac{F_e}{q} $$

\(\\ \textbf{E} = electric \hspace{4 pt} field \hspace{4 pt} strength \hspace{4 pt} (N \hspace{2 pt} C^{-1}) \\ {F_e} = electrostatic \hspace{4 pt} force \hspace{4 pt} (N) \\ \textbf{q} = charge \hspace{4 pt} (C)\)
 
$$ \large V = \frac{W}{q} $$

\(\\ \textbf{V} = potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ \textbf{W} = work \hspace{4 pt} (J) \\ \textbf{q} = charge \hspace{4 pt} (C)\)
 
$$ \large I = \frac{\Delta q}{t} $$

\(\\ \textbf{I} = current \hspace{4 pt} (A) \\ {\Delta q} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} charge \hspace{4 pt} (C) \\ \textbf{t} = time \hspace{4 pt} (s)\)
 
$$ \large I = \frac{V}{R} $$

\(\\ \textbf{I} = current \hspace{4 pt} (A) \\ \textbf{V} = potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ \textbf{R} = resistance \hspace{4 pt} (\Omega)\)
 
$$ \large R = \frac{\rho L}{A} $$

\(\\ \textbf{R} = resistance \hspace{4 pt} (\Omega) \\ {\rho} = resistivity \hspace{4 pt} (\Omega \hspace{2 pt} m) \\ \textbf{L} = length \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} conductor \hspace{4 pt} (m)\\ \textbf{A} = cross-sectional \hspace{4 pt} area \hspace{4 pt} of \\ \hspace{8 pt} the \hspace{4 pt} conductor \hspace{4 pt} (m^2) \)
 
$$ \large P = VI = I^2 R = \frac{V^2}{R} $$

\(\\ \textbf{P} = electrical \hspace{4 pt} power \hspace{4 pt} (W) \\ \textbf{V} = potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ \textbf{I} = current \hspace{4 pt} (A) \\ \textbf{R} = resistance \hspace{4 pt} (\Omega)\)
 
$$ \large W = Pt = VIt = I^2Rt = \frac{V^2t}{R} $$

\(\\ \textbf{W} = work \hspace{4 pt} (J) \\ \textbf{P} = power \hspace{4 pt} (W) \\ \textbf{t} = time \hspace{4 pt} (s) \\ \textbf{V} = potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ \textbf{I} = current \hspace{4 pt} (C)\\ \textbf{R} = resistance \hspace{4 pt} (\Omega)\)
 
$$ \large I_{tot} = I_1 = I_2 = I_3 = ... $$ $$ \large V_{tot} = V_1 + V_2 + V_3 + ... $$ $$ \large R_{tot} = R_1 + R_2 + R_3 + ... $$

\(\\ {I_{tot}} = overall \hspace{4 pt} current \hspace{4 pt} (A) \\ {I_{\#}} = current \hspace{4 pt} in \hspace{4 pt} segment \hspace{4 pt} \# \hspace{4 pt} (A) \\ {V_{tot}} = potential \hspace{4 pt} difference \hspace{4 pt} of \hspace{4 pt} circuit \hspace{4 pt} (V) \\ {V_\#} = potential \hspace{4 pt} difference \hspace{4 pt} through \\ \hspace{14 pt} segment \hspace{4 pt} \# \hspace{4 pt} (V) \\ {R_{tot}} = total \hspace{4 pt} resistance \hspace{4 pt} (\Omega) \\ {R_{\#}} = resistance \hspace{4 pt} through \hspace{4 pt} segment \hspace{4 pt} \# \hspace{4 pt} (\Omega)\)
 
$$ \large I_{tot} = I_1 + I_2 + I_3 + ... \\ $$ $$ \large V_{tot} = V_1 = V_2 = V_3 = ... \\ $$ $$ \large \frac{1}{R_{tot}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... $$

\(\\ {I_{tot}} = overall \hspace{4 pt} current \hspace{4 pt} (A) \\ {I_{\#}} = current \hspace{4 pt} in \hspace{4 pt} segment \hspace{4 pt} \# \hspace{4 pt} (A) \\ {V_{tot}} = potential \hspace{4 pt} difference \hspace{4 pt} of \hspace{4 pt} circuit \hspace{4 pt} (V) \\ {V_\#} = potential \hspace{4 pt} difference \hspace{4 pt} through \\ \hspace{14 pt} segment \hspace{4 pt} \# (V) \\ {R_{tot}} = total \hspace{4 pt} resistance \hspace{4 pt} (\Omega) \\ {R_{\#}} = resistance \hspace{4 pt} through \hspace{4 pt} segment \hspace{4 pt} \# \hspace{4 pt} (\Omega)\)
 
$$ \large c = \nu \lambda $$

\(\\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.00 \hspace{2 pt} m \hspace{2 pt} s^{-2}) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (Hz) \\ {\lambda} = wavelength \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (m)\)
 
$$ \large \theta_i = \theta_r $$

\(\\ {\theta_i} = angle \hspace{4 pt} of \hspace{4 pt} incidence \hspace{4 pt} (deg) \\ {\theta_r} = angle \hspace{4 pt} of \hspace{4 pt} reflection \hspace{4 pt} (deg)\)
 
$$ \large n = \frac{c}{v} $$

\( \textbf{n} = index \hspace{4 pt} of \hspace{4 pt} refraction \\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \\ \hspace{4 pt} (3.0 \hspace{2 pt} x \hspace{2 pt} 10^8 \hspace{4 pt} m \hspace{2 pt} s^{-1}) \\ \textbf{v} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} in \\ \hspace{8 pt} the \hspace{4 pt} substance \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \)
 
$$ \large n_1 sin \hspace{2 pt} \theta_1 = n_2 sin \hspace{2 pt} \theta_2 $$

\(\\ {n_{\#}} = absolute \hspace{4 pt} index \hspace{4 pt} of \hspace{4 pt} refraction \\ \hspace{10 pt} of \hspace{4 pt} \# \hspace{4 pt} medium \\ {\theta_{\#}} = angle \hspace{4 pt} (deg) \)
 
$$ \large \frac{n_2}{n_1} = \frac{v_1}{v_2} = \frac{{\lambda}_2}{{\lambda}_1} $$

\( n_{\#} = absolute \hspace{4 pt} index \hspace{4 pt} of \hspace{4 pt} refraction \\ \hspace{8 pt} of \# \hspace{4 pt} medium \\ n_{\#} = velocity \hspace{4 pt} in \hspace{4 pt} medium \hspace{4 pt} (m \hspace{2 pt} s^{-1} \\ \lambda_{\#} = wavelength \hspace{4 pt} in \hspace{4 pt} medium \hspace{4 pt} (m) \)
 
$$ \large E = h\nu = \frac{hc}{\lambda} $$

\( \textbf{E} = energy \hspace{4 pt} of \hspace{4 pt} a \hspace{4 pt} photon \hspace{4 pt} (J) \\ \textbf{h} = Planck's \hspace{4 pt} constant \hspace{4 pt} (6.625 \hspace{2 pt}x \hspace{2 pt} 10^{-34} J \hspace{2 pt} s ) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} light \hspace{4 pt}(Hz) \\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.0 \hspace{2 pt} x \hspace{2 pt} 10^8 \hspace{4 pt} m \hspace{2 pt} s^{-1}) \\ {\lambda} = wavelength \hspace{4 pt} (m) \)
 
$$ \large E = mc^2 $$

\(\\ \textbf{E} = energy \hspace{4 pt} (J) \\ \textbf{m} = mass \hspace{4 pt} (kg) \\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} \\ (3.00 \hspace{2 pt} x \hspace{2 pt} 10^8 \hspace{2 pt} m \hspace{2 pt} s^{-1})\)
 









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