Course Basics of Electricity and Magnetism
Electromagnetic phenomena and their applications
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Related formulas
Formula $$ I ~=~ \frac{Q}{t} $$Electric current (definition)
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Related formulas
Formula $$ W ~=~ q \, U $$Electrical Energy (Work, Voltage, Charge)
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Questions & Answers
Related formulas
Formula $$ U ~=~ R \, I $$Ohm's Law (Resistance, Voltage, Current)
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Questions & Answers
Related formulas
Formula $$ R ~=~ R_1 ~+~ R_2 ~+~ R_3 ~+~ ... $$Series circuit (total resistance, equivalent resistance)
Formula $$ \class{red}{I} ~=~ \class{red}{I_1} ~=~ \class{red}{I_2} ~=~ \class{red}{I_3} ~=~ ... ~=~ \class{red}{I_n} $$Series Circuit of Resistors (Total Current)
Formula $$ U ~=~ U_1 ~+~ U_2 ~+~ U_3 ~+~ ... ~+~ U_n $$Series Circuit of Resistors (Voltage)
Formula $$ \frac{1}{R} ~=~ \frac{1}{R_1} ~+~ \frac{1}{R_2} ~+~ \frac{1}{R_3} ~+~ ... $$Parallel connection (total resistance, equivalent resistance)
Formula $$ \class{red}{I} ~=~ \class{red}{I_1} ~+~ \class{red}{I_2} ~+~ \class{red}{I_3} ~+~ ... ~+~ \class{red}{I_n} $$Parallel Circuit of Resistors (Total Current)
Formula $$ U ~=~ U_1 ~=~ U_2 ~=~ U_3 ~=~ ... $$Parallel Circuit of Resistors (Total Voltage)
Formula $$ U_{\text{out}} = \frac{R_2}{R_1 + R_2} \, U_{\text{in}} $$Voltage Divider (Output and Input Voltage, Resistors)
Formula $$ U = \frac{\class{blue}{U_0}}{1 + \frac{R_{\text i}}{R}} $$Practical Voltage Source (Ideal Voltage, Internal Resistance)
Related Illustrations
Simple circuit with a resistor Series Connection of 3 Resistors and Their Current Series Connection of 3 Resistors and Their Voltage Parallel Connection of 3 Resistors and Their Currents Parallelschaltung von drei Widerständen und deren Spannungen Circuit with an Ideal Voltage Source Circuit with a Practical Voltage Source - 5
Related formulas
Formula $$ P ~=~ U \, I $$Electric power (voltage, current)
Formula $$ P ~=~ R \, I^2 $$Electric Power (Current, Resistance)
Formula $$ P ~=~ \frac{U^2}{R} $$Electric Power (Voltage, Resistance)
Formula $$ U ~=~ R \, I $$Ohm's Law (Resistance, Voltage, Current)
Formula $$ I ~=~ \frac{Q}{t} $$Electric current (definition)
Formula $$ W ~=~ U \, I \, t $$Electrical Energy (Voltage, Current, Time)
Related Illustrations
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Exercises with solutions
Derivations & Experiments
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Formula $$ F ~=~ \class{red}{q} \, \frac{U}{d} $$Plate Capacitor (Force, Voltage, Charge, Distance)
Formula $$ C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d} $$Plate Capacitor (Capacitance)
Formula $$ W_{\text{e}} ~=~ \frac{1}{2} \, \varepsilon_0 \, \varepsilon_{\text r} \, V \, E^2 $$Plate Capacitor (Energy, Electric Field)
Formula $$ E ~=~ \frac{U}{d} $$Plate Capacitor (Electric Field, Voltage, Distance)
Formula $$ W_{\text{e}} ~=~ \frac{1}{2} \, \frac{Q^2}{C} $$Capacitor (Energy, Capacitance, Charge)
Formula $$ W_{\text e} ~=~ \frac{1}{2} \, C \, U^2 $$Capacitor (Energy, Voltage, Capacitance)
Formula $$ \varphi_x = - \frac{U}{d} \, x ~+~ \varphi_1 $$Plate capacitor (potential, voltage, distance)
Formula $$ F ~=~ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2d^2}\, U^2 $$Plate Capacitor (Attraction Force, Voltage)
Formula $$ F ~=~ \frac{Q^2}{2\varepsilon_0 \, \varepsilon_{\text r} A^2} $$Plate Capacitor (Attraction Force, Charge)
Related Illustrations
Charged Plate Capacitor with Dielectric Material Electric force on a charge in a plate capacitor Plate capacitor - field lines (inside / outside) Electric field inside / outside (Graph) - Plate capacitor Electrical potential inside / outside a plate capacitor (graph) Energy in the E-Field of a Charged Plate Capacitor - 7
Exercises with solutions
Related formulas
Formula $$ I(t) ~=~ I_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$Charging Capacitor (Current, Capacitance, Resistance, Time)
Formula $$ U_{\text C}(t) ~=~ U_0 \, \left(1 - \mathrm{e}^{-\frac{t}{\class{brown}{R}\,C}}\right) $$Charging Capacitor (Voltage, Capacitance, Resistance, Time)
Formula $$ U_{\text R}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$Charging a Capacitor (Voltage at the Resistor)
Formula $$ U_{\text C}(t) ~=~ U_0 \, \mathrm{e}^{-\frac{t}{R\,C} } $$Discharging Capacitor (Voltage, Capacitance, Resistance, Time)
Formula $$ I(t) ~=~ -I_0 \, \mathrm{e}^{-\frac{t}{R\,C}} $$Discharging Capacitor (Discharge Current, Capacitance, Resistance, Time)
Formula $$ t_{\text h} ~=~ R\,C \, \ln(2) $$RC Circuit (Half-Life)
Formula $$ \tau ~=~ R \, C $$RC Circuit (Time Constant)
Related Illustrations
RC Circuit: Charging Capacitor RC Circuit: Discharging Capacitor Current-Time Graph: Charging a Capacitor Voltage-Time Graph: Charging Capacitor Voltage-Time Graph of Resistor - Charging a Capacitor Current-Time Graph: Discharging a Capacitor Voltage-Time Graph: Discharging a Capacitor Voltage-Time Graph of a Series Resistor During Discharge of a Capacitor - 8
Related formulas
Formula $$ \class{purple}{X_{\text C}} ~=~ -\frac{1}{2\pi \, f \, \class{purple}{C}} $$Capacitive Reactance (Capacitance, Frequency)
Related Illustrations
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Related formulas
Formula $$ \class{brown}{X_{\text L}} ~=~ 2 \pi \, f \, \class{brown}{L} $$Inductive Reactance (Inductance, Frequency)
Related Illustrations
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Related Illustrations
Left and Right Hand Rule using 3 Fingers Moving Electric Charge Magnetic Field Direction in a Horseshoe Magnet Symbols for the magnetic field direction perpendicular to the plane Lorentz force on a positive charge in the magnetic field Lorentz force on a negative charge in the magnetic field Current in the Conductor Swing in the Horseshoe Magnet - 11
Exercises with solutions
Derivations & Experiments
Related formulas
Formula $$ \class{green}{F} ~=~ q \, \class{blue}{v} \, \class{violet}{B} $$Lorentz Force (Magnetic field, Velocity)
Formula $$ \class{green}{F} ~=~ q \, \class{blue}{v} \, \class{violet}{B} \, \sin(\alpha) $$Lorentz Force (Angle, Magnetic Field, Velocity)
Formula $$ r ~=~ \frac{ \class{brown}{m} \, \class{blue}{v} }{ |q| \, \class{violet}{B} } $$Circular Motion in a Magnetic Field (Radius, Velocity, Mass)
Formula $$ f ~=~ \frac{|q| \, \class{violet}{B}}{2\pi \, \class{brown}{m}} $$Cyclotron Frequency (B-field, Charge, Mass)
Formula $$ T ~=~ 2 \, \pi \frac{ \class{brown}{m} }{ |q| \, \class{violet}{B} } $$Circular Motion in the Magnetic Field (Period, Charge, Mass)
Formula $$ \class{green}{F} ~=~ \class{blue}{I} \, L \, \class{violet}{B} $$Current-Carrying Wire in Magnetic Field (Force, Current, Length)
Formula $$ \class{green}{F} ~=~ \frac{\mu_0 \, L}{2 \pi} \, \frac{ \class{blue}{I_1} \, \class{blue}{I_2} }{r} $$Two Current-Carrying Wires (Force, Current, Distance)
Related Illustrations
Lorentz Force: Electron in a Magnetic Field Electron in magnetic field perpendicular to direction of motion Electron movement at an angle to the magnetic field Spiral motion of an electron in a magnetic field Cross product between velocity and magnetic field Lorentz force on a current-carrying wire in a magnetic field Attractive Lorentz force - two current-carrying wires of the same direction Repulsive Lorentz force - two conductors with current flowing in opposite directions - 12
Related formulas
Formula $$ \class{green}{F} ~=~ q \, \class{blue}{v} \, \class{violet}{B} $$Lorentz Force (Magnetic field, Velocity)
Formula $$ F_{ \text z} ~=~ \frac{\class{brown}{m} \, \class{blue}{v}^2}{ r } $$Circular motion (centripetal force, velocity, radius)
Formula $$ \frac{q}{\class{brown}{m}} ~=~ \frac{ \class{red}{v} }{ r \, \class{violet}{B}} $$Specific Charge (Magnetic Field, Velocity, Radius)
Formula $$ \frac{q}{\class{brown}{m}} ~=~ \frac{2 \, U_{\text B}}{r^2 \, \class{violet}{B}^2} $$Specific Charge (Voltage, Magnetic Field, Radius)
Related Illustrations
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Related formulas
Formula $$ \class{green}{F} ~=~ q \, \class{blue}{v} \, \class{violet}{B} $$Lorentz Force (Magnetic field, Velocity)
Formula $$ F ~=~ \class{red}{q} \, E $$Charge in an Electric Field (Force, Charge)
Related Illustrations
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Derivations & Experiments
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Formula $$ U_{\text H} ~=~ A_{\text H} \, \frac{I \, \class{violet}{B}}{d} $$Hall Effect (Voltage, Hall Coefficient, Current, B-Field)
Formula $$ U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d} $$Hall Effect (Hall Voltage, Charge Carrier Density)
Formula $$ U_\text{H} ~=~ v \, \class{violet}{B} \, h $$Hall Effect (Voltage, Drift Velocity)
Formula $$ A_{\text H} ~=~ \frac{ \class{red}{p} \,{\mu_{\text +}}^2 ~-~ \class{blue}{n} \, {\mu_{\text -}}^2}{e \, (\class{red}{p} \, \mu_{\text +} ~+~ \class{blue}{n} \, \mu_{\text -})^2} $$Hall constant (Electron and Hole Mobilities, Charge Carrier Density)
Related Illustrations
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Related formulas
Formula $$ \frac{1}{C} ~=~ \frac{1}{C_1} ~+~ \frac{1}{C_2} ~+~... ~+~ \frac{1}{C_n} $$Series circuit of capacitors (capacitance)
Formula $$ U ~=~ U_1 ~+~ U_2 ~+~ U_3 ~+~ ... ~+~ U_n $$Series Circuit of Capacitors (Voltage)
Formula $$ \class{red}{Q} ~=~ \class{red}{Q_1} ~=~ \class{red}{Q_2} ~=~ \class{red}{Q_3} ~=~ ... ~=~ \class{red}{Q_n} $$Series Circuit of Capacitors (Charge)
Formula $$ C ~=~ C_1 ~+~ C_2 ~+~ ...~+~ C_n $$Parallel connection (total capacitance / equivalent capacitance)
Formula $$ \class{red}{Q} ~=~ \class{red}{Q_1} ~+~ \class{red}{Q_2} ~+~ \class{red}{Q_3} ~+~ ... ~+~ \class{red}{Q_n} $$Parallel Circuit of Capacitors (Charge)
Formula $$ U ~=~ U_1 ~=~ U_2 ~=~ U_3 ~=~ ... ~=~ U_n $$Parallel Circuit of Capacitors (Voltage)
Related Illustrations
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Related formulas
Formula $$ L ~=~ L_1 ~+~ L_2 ~+~ ... ~+~ L_n $$Series circuit of coils (inductance)
Formula $$ \frac{1}{L} ~=~ \frac{1}{L_1} ~+~ \frac{1}{L_2} ~+~ ... ~+~ \frac{1}{L_n} $$Parallel circuit of coils (inductance)
Related Illustrations
