Physics/Synopsis

Force

 * {|width=90%


 * Force 
 * Symbol
 * Mathematical Formula
 * Opposing Force
 * $$F_-$$
 * $$-F$$
 * Gravity Force
 * $$F_g$$
 * $$G \frac{Mm}{r^2}$$
 * Motion Force
 * $$F_a$$
 * $$m a = m \frac{v}{t} = \frac{p}{t}$$
 * Pressure Force
 * $$F_A$$
 * $$\frac{F}{A}$$
 * Elastic Force
 * $$F_x$$
 * $$-k x$$
 * Circulation Force
 * $$F_r$$
 * $$mvr=pr$$
 * Centripetal Force
 * $$F_c$$
 * $$m\frac{v^2}{r}$$
 * Electrostatic Force
 * $$F_q$$
 * $$\frac{q_+ q_-}{r^2}$$
 * Electromotive force
 * $$F_E$$
 * $$qE$$
 * Electromagnetomotive Force
 * $$F_B$$
 * $$\pm qvB$$
 * Electromagnetic Force
 * $$F_{EB}$$
 * $$q(E \pm vB)$$
 * }
 * Electromotive force
 * $$F_E$$
 * $$qE$$
 * Electromagnetomotive Force
 * $$F_B$$
 * $$\pm qvB$$
 * Electromagnetic Force
 * $$F_{EB}$$
 * $$q(E \pm vB)$$
 * }
 * $$q(E \pm vB)$$
 * }

Linear Motion

 * O > O


 * {|width=80%


 * Distance || $$s$$ || $$vt $$
 * Time || $$t$$ || $$t$$
 * Speed || $$v$$ || $$\frac{s}{t} $$
 * Accelleration || $$a$$ || $$\frac{v}{t} $$
 * Force || $$F$$ || $$m \frac{v}{t}$$
 * Work || $$W$$ || $$F s$$
 * Energy || $$E$$ ||$$\frac{W}{t}$$
 * }
 * Force || $$F$$ || $$m \frac{v}{t}$$
 * Work || $$W$$ || $$F s$$
 * Energy || $$E$$ ||$$\frac{W}{t}$$
 * }
 * Energy || $$E$$ ||$$\frac{W}{t}$$
 * }
 * }
 * }


 * O
 * O
 * O


 * {|width=70%


 * Distance || $$s$$ || $$h $$
 * Time || $$t$$ || $$t$$
 * Speed || $$v$$ || $$\frac{h}{t} $$
 * Accelleration || $$a$$ || $$\frac{h}{t^2} $$
 * Force || $$F$$ || $$m g$$
 * Work || $$W$$ || $$m g h$$
 * Energy || $$E$$ ||$$\frac{m g h}{t}$$
 * }
 * Force || $$F$$ || $$m g$$
 * Work || $$W$$ || $$m g h$$
 * Energy || $$E$$ ||$$\frac{m g h}{t}$$
 * }
 * Energy || $$E$$ ||$$\frac{m g h}{t}$$
 * }
 * }
 * }


 * Non-Uniform linear motion
 * {|width=100%


 * Distance || $$s$$ || $$(v_o + at)t $$
 * Time || $$t$$ || $$t$$
 * Speed || $$v$$ || $$v_o + at $$
 * Accelleration || $$a$$ || $$\frac{\Delta v}{\Delta t}$$
 * Force || $$F$$ || $$m \frac{\Delta v}{\Delta t}$$
 * Work || $$W$$ || $$F t (v_o+at)$$
 * Energy || $$E$$ ||$$F (v_o+at)$$
 * }
 * Force || $$F$$ || $$m \frac{\Delta v}{\Delta t}$$
 * Work || $$W$$ || $$F t (v_o+at)$$
 * Energy || $$E$$ ||$$F (v_o+at)$$
 * }
 * Energy || $$E$$ ||$$F (v_o+at)$$
 * }
 * }
 * }

Non Linear Motion

 * {|width=100%


 * Distance || $$s(t)$$||$$\int v(t) dt$$
 * Time || $$t$$ || $$t$$
 * Speed || $$v(t)$$||$$v(t)$$
 * Acceleration ||$$a(t)$$||$$\frac{d}{dt}v(t)$$
 * Force ||$$F(t)$$ || $$m \frac{d}{dt}v(t)$$
 * Work ||$$W(t)$$ || $$F \int v(t) dt$$
 * Energy ||$$E(t)$$ || $$\frac{F}{t} \int v(t) dt$$
 * }
 * Force ||$$F(t)$$ || $$m \frac{d}{dt}v(t)$$
 * Work ||$$W(t)$$ || $$F \int v(t) dt$$
 * Energy ||$$E(t)$$ || $$\frac{F}{t} \int v(t) dt$$
 * }
 * Energy ||$$E(t)$$ || $$\frac{F}{t} \int v(t) dt$$
 * }
 * }
 * }
 * }

Circular Motion

 * Circle-withsegments.svgUniform_circular_motion.svgVelocity-acceleration.PNG


 * Complete full circle
 * {|width=100%


 * Distance || $$s$$ || $$2 \pi r$$
 * Time|| $$t$$ || $$t$$
 * Speed || $$v$$ || $$r \frac{2 \pi}{t} = r \omega$$
 * Acceleration|| $$a$$ || $$\frac{r \omega}{t}$$
 * Angular spped ||  $$\omega$$ || $$\frac{2 \pi}{t} = 2 \pi f = \frac{v}{r}$$
 * Frequency || $$f$$ || $$\frac{1}{t}$$
 * Force || $$F$$ || $$m \frac{r \omega}{t}$$
 * Work || $$W $$ || $$p r \omega$$
 * Energy || $$E$$ || $$\frac{p r \omega}{t}$$
 * }
 * Frequency || $$f$$ || $$\frac{1}{t}$$
 * Force || $$F$$ || $$m \frac{r \omega}{t}$$
 * Work || $$W $$ || $$p r \omega$$
 * Energy || $$E$$ || $$\frac{p r \omega}{t}$$
 * }
 * Work || $$W $$ || $$p r \omega$$
 * Energy || $$E$$ || $$\frac{p r \omega}{t}$$
 * }
 * }


 * Circle's arc
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 * Distance || $$s$$ || $$r \theta$$
 * Time|| $$t$$ || $$t$$
 * Speed || $$v$$ || $$r \frac{\theta}{t} $$
 * Acceleration|| $$a$$ || $$\frac{r \theta}{t^2}$$
 * Force || $$F$$ || $$m \frac{r \theta}{t^2}$$
 * Work || $$W $$ || $$p r \frac{\theta}{t} $$
 * Energy || $$E$$ || $$\frac{p r \theta}{t^2}$$
 * }
 * Force || $$F$$ || $$m \frac{r \theta}{t^2}$$
 * Work || $$W $$ || $$p r \frac{\theta}{t} $$
 * Energy || $$E$$ || $$\frac{p r \theta}{t^2}$$
 * }
 * Energy || $$E$$ || $$\frac{p r \theta}{t^2}$$
 * }
 * }

Characteristics

 * $$F = m a = m \frac{v}{t} = \frac{p}{t} $$
 * $$p = m v = F t $$

Momentum of a mass

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 * Speed || $$v$$ || $$v $$
 * Mass||$$m$$ || $$m $$
 * Momentum || $$p$$ || $$m v = F t$$
 * Force || $$F$$ || $$m a = m \frac{v}{t} = \frac{p}{t}$$
 * Work || $$W$$ || $$F s = F v t = p v$$
 * Energy || $$E$$ || $$F v = F a t = p a$$
 * }
 * Force || $$F$$ || $$m a = m \frac{v}{t} = \frac{p}{t}$$
 * Work || $$W$$ || $$F s = F v t = p v$$
 * Energy || $$E$$ || $$F v = F a t = p a$$
 * }
 * Energy || $$E$$ || $$F v = F a t = p a$$
 * }
 * }

Momentum of a relativistic mass

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 * Speed || $$v$$ || $$\gamma = \sqrt{1 - \frac{v^2}{C^2}} $$
 * Mass||$$m$$ || $$m_o(\gamma-1) $$
 * Momentum || $$p$$ || $$m v $$
 * Energy || $$E$$ || $$pv$$
 * }
 * Momentum || $$p$$ || $$m v $$
 * Energy || $$E$$ || $$pv$$
 * }
 * }
 * }

Momentum of a massless quanta

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 * Speed || $$v$$ || $$C = \lambda f $$
 * Mass||$$m$$ || $$h = p \lambda $$
 * Energy || $$E$$ || $$pv = pC=p \lambda f = h f$$
 * Momentum || $$p$$ || $$\frac{h}{\lambda}$$
 * Wavelength || $$\lambda$$ || $$\frac{h}{p} = \frac{C}{f}$$
 * }
 * Momentum || $$p$$ || $$\frac{h}{\lambda}$$
 * Wavelength || $$\lambda$$ || $$\frac{h}{p} = \frac{C}{f}$$
 * }
 * Wavelength || $$\lambda$$ || $$\frac{h}{p} = \frac{C}{f}$$
 * }
 * }

Momentum of an electric charge in circle

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 * Equilibrium || $$QvB = p \frac{v}{r}$$
 * Speed || $$v = \frac{Q}{m}Br$$
 * Radius || $$r = \frac{p}{QB}$$
 * }
 * Radius || $$r = \frac{p}{QB}$$
 * }
 * }

Momentum of atom's free electron

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 * Equilibrium || $$hf=hf_o+\frac{1}{2} m v^2$$
 * Speed || $$v = \sqrt{\frac{2}{m}(hf-hf_o)} = \sqrt{\frac{2}{m}(nhf_o)}$$ With $$f > f_o = nf_o$$ to have $$v>0$$
 * }
 * Speed || $$v = \sqrt{\frac{2}{m}(hf-hf_o)} = \sqrt{\frac{2}{m}(nhf_o)}$$ With $$f > f_o = nf_o$$ to have $$v>0$$
 * }
 * }

Momentum of a bind electron

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 * Equilibrium || $$nhf=mvr 2\pi$$
 * Speed || $$v = \frac{1}{2 \pi} \frac{nhf}{mr}$$
 * Radius || $$r = \frac{1}{2 \pi} \frac{nhf}{mv}$$
 * Potential Energy Level n || $$n = 2 \pi \frac{mv}{hf}$$
 * }
 * Radius || $$r = \frac{1}{2 \pi} \frac{nhf}{mv}$$
 * Potential Energy Level n || $$n = 2 \pi \frac{mv}{hf}$$
 * }
 * }
 * }

AC electrical sinusoidal wave generator
An interaction of 2 electromagnets creates an AC electricity that has amplitude varies sinusoidally
 * $$v(t) = A Sin (\omega t + \theta)$$
 * Alternator_1.svg

LC sinusoidal wave generator

 * Series_LC_Circuit.svg

Series LC operates at equilibrium satisfy wave equation
 * $$\frac{d^2}{dt^2} i(t) = - \frac{1}{T} i(t)$$

that has root of a sinusoidal wave function
 * FreqWave1.png
 * $$i(t) = A Sin \omega t$$
 * $$\omega = \sqrt{\frac{1}{T}}$$
 * $$T = LC$$

Electromagnetic sinusoidal wave generator

 * VFPt_Solenoid_correct2.svg

A coil of N turns operates at equilibrium satisfy wave equation
 * $$\nabla^2 E(t) = - \omega E(t)$$
 * $$\nabla^2 B(t) = - \omega B(t)$$

that has root of a sinusoidal wave function
 * Onde_electromagnetique.svg
 * $$E(t) = A Sin \omega t$$
 * $$B(t) = A Sin \omega t$$


 * $$\omega = \sqrt{\frac{1}{T}} = C = \lambda f$$
 * $$T = \mu \epsilon$$

Wave Characteristics

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 * Distance || $$s$$ || $$\lambda$$
 * Time|| $$t$$ || $$t$$
 * Speed || $$v$$ || $$\frac{\lambda}{t} $$
 * Angular speed||$$\omega$$ || $$2 \pi f $$
 * Frequency || $$f$$ || $$\frac{1}{t}$$
 * Sinusoidal wave equation || $$f^{''}(t)$$ || $$- \omega f(t)$$
 * Sinusoidal wave function || $$f(t)$$ || $$A Sin \omega t$$
 * }
 * Frequency || $$f$$ || $$\frac{1}{t}$$
 * Sinusoidal wave equation || $$f^{''}(t)$$ || $$- \omega f(t)$$
 * Sinusoidal wave function || $$f(t)$$ || $$A Sin \omega t$$
 * }
 * Sinusoidal wave function || $$f(t)$$ || $$A Sin \omega t$$
 * }
 * }

Wave types

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 * Wave || 2 dimensional sinusoidal wave || 3 dimensional sinusoidal plane wave
 * || FreqWave1.png || Onde_electromagnetique.svg
 * Wave oscillation equation || $$\frac{d^2}{dt^2} f(t) = -\omega f(t)$$
 * Wave function || $$f(t) = A Sin \omega t$$ || $$E(t) = A Sin \omega t$$ $$B(t) = A Sin \omega t$$ $$\omega = \sqrt{\frac{1}{T}} = C = \lambda f$$ $$T = \mu \epsilon$$
 * }
 * Wave oscillation equation || $$\frac{d^2}{dt^2} f(t) = -\omega f(t)$$
 * Wave function || $$f(t) = A Sin \omega t$$ || $$E(t) = A Sin \omega t$$ $$B(t) = A Sin \omega t$$ $$\omega = \sqrt{\frac{1}{T}} = C = \lambda f$$ $$T = \mu \epsilon$$
 * }
 * }
 * }

Electricity Types

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 * Electricity types  || Definition  || Mathematical Formula  || Source
 * DC Electricity || Electricity that provides constant voltage over time || $$v(t) = V$$ || Electrolysis, Electrochemcial Cell, PhotonVoltaic
 * AC Electricity || Electricity that provides sinusoidal changing voltage over changing time || $$v(t) = V Sin \omega t$$ || Electromagnetic induction
 * }
 * AC Electricity || Electricity that provides sinusoidal changing voltage over changing time || $$v(t) = V Sin \omega t$$ || Electromagnetic induction
 * }
 * }
 * }

DC & AC Response

 * Resistor circuit
 * {|width=80%


 * Characteristics|| DC || AC
 * Voltage || $$V = I R$$ || $$v = i R$$
 * Current || $$I =\frac{V}{R}$$ || $$i =\frac{v}{R}$$
 * Resistance || $$R = \frac{V}{I}$$ || $$R = \frac{v}{i}$$
 * Power provided || $$P_V = I V $$ || $$P_V = i v $$
 * Power Loss || $$P_R = I^2 R(T) = \frac{V^2}{R(T)}$$ || $$P_R = i^2 R(T) = \frac{v^2}{R(T)}$$
 * Power delivered|| $$P = P_V - P_R$$
 * Reactance || || $$X_R=0$$
 * Impedance || || $$Z_R = X_R + R = R$$
 * Phase || || $$0$$
 * Power Loss || $$P_R = I^2 R(T) = \frac{V^2}{R(T)}$$ || $$P_R = i^2 R(T) = \frac{v^2}{R(T)}$$
 * Power delivered|| $$P = P_V - P_R$$
 * Reactance || || $$X_R=0$$
 * Impedance || || $$Z_R = X_R + R = R$$
 * Phase || || $$0$$
 * Reactance || || $$X_R=0$$
 * Impedance || || $$Z_R = X_R + R = R$$
 * Phase || || $$0$$
 * Phase || || $$0$$
 * Phase || || $$0$$


 * }


 * Capacitor circuit
 * {|width=100%


 * Characteristics|| DC || AC
 * Voltage || $$V = Q C = \frac{W}{Q}$$ || $$v = \frac{1}{C} \int i dt$$
 * Charge || $$Q = \frac{V}{C}$$
 * Capacitance|| $$C = \frac{V}{Q}$$
 * Current || $$I = \frac{Q}{t}$$ || $$i = C \frac{dv}{dt}$$
 * Power provided || $$P_V = I V = (\frac{Q}{t}) (\frac{W}{Q}) = \frac{W}{t}$$ ||$$p = \frac{1}{2} Cv^2$$
 * Reactance || || $$X_C(t) = \frac{v}{i}$$ $$X_C(j \omega) = \frac{1}{j \omega C}$$ $$X_C(\omega \theta) = \frac{1}{\omega C} \angle -90$$
 * Impedance || || $$Z_C(t) = X_C + R_C$$ $$X_C(j \omega) = \frac{1}{j \omega C} + R_C $$ $$X_C(\omega \theta) = \frac{1}{\omega C} \angle -90 + R \angle 0 $$
 * Phase || ||$$Tan \theta = \frac{1}{\omega T}$$
 * Time Constant || || $$T = CR_C$$
 * }
 * Reactance || || $$X_C(t) = \frac{v}{i}$$ $$X_C(j \omega) = \frac{1}{j \omega C}$$ $$X_C(\omega \theta) = \frac{1}{\omega C} \angle -90$$
 * Impedance || || $$Z_C(t) = X_C + R_C$$ $$X_C(j \omega) = \frac{1}{j \omega C} + R_C $$ $$X_C(\omega \theta) = \frac{1}{\omega C} \angle -90 + R \angle 0 $$
 * Phase || ||$$Tan \theta = \frac{1}{\omega T}$$
 * Time Constant || || $$T = CR_C$$
 * }
 * Phase || ||$$Tan \theta = \frac{1}{\omega T}$$
 * Time Constant || || $$T = CR_C$$
 * }
 * }
 * }


 * Inductor circuit
 * {|width=80%


 * Characteristics || DC || AC
 * Magnetic Field Strength || $$B = L I$$
 * Current || $$I = \frac{B}{L}$$
 * Inductance || $$C = \frac{B}{I}$$
 * Current || $$I = \frac{Q}{t}$$
 * Power provided || $$P_V = I V = (\frac{B}{l}) (\frac{W}{Q}) = \frac{W}{t}$$ ||
 * Reactance || || $$X_L(t) = \frac{v}{i}$$ $$X_L(j \omega) = j \omega L$$ $$X_L(\omega \theta) = \omega L \angle 90$$
 * Impedance || || $$Z_C(t) = X_C + R_C$$ $$X_C(j \omega) = j \omega L + R_L $$ $$X_C(\omega \theta) = \omega L \angle 90 + R \angle 0 $$
 * Phase || ||$$Tan \theta = \omega T$$
 * Time Constant || || $$T = \frac{L}{R_L}$$
 * }
 * Power provided || $$P_V = I V = (\frac{B}{l}) (\frac{W}{Q}) = \frac{W}{t}$$ ||
 * Reactance || || $$X_L(t) = \frac{v}{i}$$ $$X_L(j \omega) = j \omega L$$ $$X_L(\omega \theta) = \omega L \angle 90$$
 * Impedance || || $$Z_C(t) = X_C + R_C$$ $$X_C(j \omega) = j \omega L + R_L $$ $$X_C(\omega \theta) = \omega L \angle 90 + R \angle 0 $$
 * Phase || ||$$Tan \theta = \omega T$$
 * Time Constant || || $$T = \frac{L}{R_L}$$
 * }
 * Phase || ||$$Tan \theta = \omega T$$
 * Time Constant || || $$T = \frac{L}{R_L}$$
 * }
 * }
 * }


 * Electric Decay
 * {|width=100%


 * RL_Series_Open-Closed.svg || $$\frac{d}{dt} i = -\frac{1}{T} i$$ || $$i = A e^{-\frac{1}{T} t}$$ || ||$$T=\frac{L}{R}$$
 * RC_switch.svg || $$\frac{d}{dt} v = -\frac{1}{T} v$$ || $$v = A e^{-\frac{1}{T} t}$$ || ||$$T=RC$$
 * }
 * RC_switch.svg || $$\frac{d}{dt} v = -\frac{1}{T} v$$ || $$v = A e^{-\frac{1}{T} t}$$ || ||$$T=RC$$
 * }


 * Electric Oscillation
 * {|width=100%


 * Modes of Oscillation|| Oscillation equation || Wave Function || Angular Speed || Oscillation Time Constant || Oscilation Constant || Decay Constant ' || Decay Time Constant
 * Electric decay current sinusoidal wave oscillation RLC_series_circuit_v1.svg || $$\frac{d^2}{dt^2} i = -2\alpha\frac{d}{dt}i - \beta i$$ || $$i = A(\alpha) Sin \omega t$$ ||$$\omega=\sqrt{\beta - \alpha}$$ || $$T=LC$$ || $$\beta=\frac{1}{T}$$|| $$\alpha=\beta \gamma$$|| $$\gamma= RC$$
 * Electric peak current sinusoidal wave oscillation RLC_series_circuit_v1.svg || $$Z_L = - Z_C$$ $$Z_t = R$$ || $$i(\omega=0)=0$$ $$i(\omega=\omega_o)=\frac{v}{2}$$ $$i(\omega=00)=0$$ || $$\omega_o =\sqrt{\frac{1}{T}}$$|| $$T=LC$$
 * Electric current sinusoidal wave oscillation Series_LC_Circuit.svg || $$\frac{d^2}{dt^2} i = -\frac{1}{T} i$$ || $$i = A Sin \omega t$$ ||$$\omega=\sqrt{\frac{1}{T}}$$ || $$T=LC$$
 * Electric current sinusoidal standing wave oscillation Series_LC_Circuit.svg || $$Z_L = - Z_C$$ || $$V_L = - V_C$$ || $$\omega_o=\sqrt{\frac{1}{T}}$$ || $$T=LC$$
 * }
 * Electric current sinusoidal wave oscillation Series_LC_Circuit.svg || $$\frac{d^2}{dt^2} i = -\frac{1}{T} i$$ || $$i = A Sin \omega t$$ ||$$\omega=\sqrt{\frac{1}{T}}$$ || $$T=LC$$
 * Electric current sinusoidal standing wave oscillation Series_LC_Circuit.svg || $$Z_L = - Z_C$$ || $$V_L = - V_C$$ || $$\omega_o=\sqrt{\frac{1}{T}}$$ || $$T=LC$$
 * }
 * Electric current sinusoidal standing wave oscillation Series_LC_Circuit.svg || $$Z_L = - Z_C$$ || $$V_L = - V_C$$ || $$\omega_o=\sqrt{\frac{1}{T}}$$ || $$T=LC$$
 * }
 * }

Electric charge

 * {|width=100%


 * Charge acquired process || Electric charge || Charge quantity || Electric field || Magnetic field
 * Matter + e- || - || -Q || -->E<-- || B ↓
 * Matter - e- || + || +Q || <--E--> || B ↑
 * }
 * Matter - e- || + || +Q || <--E--> || B ↑
 * }
 * }
 * }

Electromagnetic force

 * {|width=100%


 * Force || Symbol || Mathematical formula
 * Electrostatic Force || $$F_q$$ || $$K \frac{q_+ q_-}{r^2}$$
 * Electromotive Force || $$F_E$$ || $$q E$$
 * Electromagnetomotive Force || $$F_B$$ || $$\pm q v B$$
 * Electromagnetic Force || $$F_{EB}$$ || $$qE \pm q vB = q(E\pm B)$$
 * }
 * Electromagnetomotive Force || $$F_B$$ || $$\pm q v B$$
 * Electromagnetic Force || $$F_{EB}$$ || $$qE \pm q vB = q(E\pm B)$$
 * }
 * Electromagnetic Force || $$F_{EB}$$ || $$qE \pm q vB = q(E\pm B)$$
 * }

Electromagnetic Field

 * {|width=100%


 * Configuration  || Symbol  || Mathematical Formulas
 * For any configuration || $$B$$ || $$B = L I$$
 * For straight line conductor || $$B$$ || $$B = L I = \frac{\mu}{2 \pi r} I$$ || Circular B field
 * For circular loop conductor || $$B$$ || $$B = L I = \frac{\mu}{2 r} I$$ || Circular B field around a point charge
 * For coil of N circular loops conductor ||  $$B$$ || $$B = L I = \frac{N \mu}{l} I$$ || Eleptic B field around the coil
 * }
 * For circular loop conductor || $$B$$ || $$B = L I = \frac{\mu}{2 r} I$$ || Circular B field around a point charge
 * For coil of N circular loops conductor ||  $$B$$ || $$B = L I = \frac{N \mu}{l} I$$ || Eleptic B field around the coil
 * }
 * For coil of N circular loops conductor ||  $$B$$ || $$B = L I = \frac{N \mu}{l} I$$ || Eleptic B field around the coil
 * }
 * }

Electromagnetic Principles

 * {|width=100%


 * || ||VFPt_Solenoid_correct2.svg
 * Electromagnetic field || $$B$$ || $$L I$$
 * Induced electromagnetic field  || $$\phi$$ || $$-NB=-NLI$$
 * Electromagnetization field || $$H$$ || $$\frac{B}{\mu} = \frac{\phi}{N\mu}$$
 * Eletromagnetization || || $$\nabla \cdot D = \rho$$ $$\nabla \times E = -\nabla B$$ $$\nabla \cdot B = 0$$ $$\nabla \times H = J + \nabla B$$
 * }
 * {|width=90%
 * Electromagnetization field || $$H$$ || $$\frac{B}{\mu} = \frac{\phi}{N\mu}$$
 * Eletromagnetization || || $$\nabla \cdot D = \rho$$ $$\nabla \times E = -\nabla B$$ $$\nabla \cdot B = 0$$ $$\nabla \times H = J + \nabla B$$
 * }
 * {|width=90%
 * {|width=90%


 * Coil's voltage induction intencity || $$V$$ || $$V = \frac{dB}{dt} = L \frac{dI}{dt}$$
 * Turn's induced voltage intencity || $$\epsilon$$ || $$-\frac{d\phi}{dt}=-N\frac{dB}{dt}=-NL\frac{d}{dt}I$$
 * }
 * Turn's induced voltage intencity || $$\epsilon$$ || $$-\frac{d\phi}{dt}=-N\frac{dB}{dt}=-NL\frac{d}{dt}I$$
 * }


 * {|width=80%


 * Electromagnetic oscillation || || $$\nabla \cdot E = 0$$ $$\nabla \times E = \frac{1}{T}$$ $$\nabla \cdot B = 0$$ $$\nabla \times B = \frac{1}{T}$$
 * Electromagnetic wave Onde_electromagnetique.svg || || $$\nabla^2 E = - \omega E$$ $$\nabla^2 B = - \omega B$$ $$E =  A Sin \omega t$$ $$B =  A Sin \omega t$$ $$\omega=\sqrt{\frac{1}{T}}=C=\lambda f$$ $$T=\mu \epsilon$$
 * Electromagnetic wave radiation || || $$v=\omega=\sqrt{\frac{1}{\mu \epsilon}}=C=\lambda f$$ $$E=pv=pC=p \lambda f= h f$$ $$h=p \lambda$$ $$p = \frac{h}{\lambda}$$ $$\lambda=\frac{h}{p}=\frac{C}{f}$$
 * }
 * Electromagnetic wave radiation || || $$v=\omega=\sqrt{\frac{1}{\mu \epsilon}}=C=\lambda f$$ $$E=pv=pC=p \lambda f= h f$$ $$h=p \lambda$$ $$p = \frac{h}{\lambda}$$ $$\lambda=\frac{h}{p}=\frac{C}{f}$$
 * }
 * }

Photon
Photon is defined as energy of a massless quanta travels as an electromagnetic oscillation wave radiation at speed equal to speed of light Mathematical formula of
 * $$ E = hf = \hbar \omega$$

Photon exist in 2 states
 * Radiant Photon at threshold frequency fo
 * $$ E = hf_o = \hbar \omega_o$$
 * Non Radiant Photon at frequency greater than threshold frequency fo
 * $$ E = hf = \hbar \omega$$ . With f>fo

Photon can only exist in one state at a time. This is Heiseinberg's uncertainty principle the success rate of finding photon
 * $$\Delta p \Delta \lambda = \frac{1}{2} \frac{h}{2 \pi} = \frac{\hbar}{2}$$

Quanta of Photon
Quantity of photon's energy. Quanta is denoted as h measured in has a constant value h =
 * $$h = p \lambda$$

Quanta process Wave particle duality meaning
 * Sometimes it behaves like wave $$\lambda=\frac{h}{p}$$
 * Sometimes it behaves like particle $$p=\frac{h}{\lambda}$$

Photon and matter
Photon and matter interacts to create Heat transfer through 3 phases Heat conduction, Heat convection and Heat radiation
 * {|width=100%


 * Heat transfer || || ||
 * Heat conduction || Matter changes it's temperature while absorb heat energy || $$\Delta T = T_1-T_0$$ $$E=mC \Delta T$$
 * Heat convection  || Matter conducts heat energy to the max at Threshold frequency fo || $$f_o=\frac{C}{f_o}$$ $$E=hf_o$$
 * Heat radiation || Matter uses excess energy above maximum absorbing energy to release electron off atom || $$hf-hf_o = \frac{1}{2}m v^2$$. When v>0 $$v=\sqrt{\frac{2}{m} nhf_o}$$ with f > fo
 * }
 * Heat convection  || Matter conducts heat energy to the max at Threshold frequency fo || $$f_o=\frac{C}{f_o}$$ $$E=hf_o$$
 * Heat radiation || Matter uses excess energy above maximum absorbing energy to release electron off atom || $$hf-hf_o = \frac{1}{2}m v^2$$. When v>0 $$v=\sqrt{\frac{2}{m} nhf_o}$$ with f > fo
 * }
 * }
 * }

Causes matter to decay through 3 kinds of decays
 * {|width=100%


 * Mattter decay  || Reaction  ||
 * Alpha decay || Ur--> Th - He + Alpha radiation ||
 * Beta decay || C-->N + Beta radiation
 * Gamma decay || ee) + Gamma radiation
 * }
 * Beta decay || C-->N + Beta radiation
 * Gamma decay || ee) + Gamma radiation
 * }
 * }

Experiment has shown that, electron of an atom can be freed or binded from absorbing or releasing photon's energy
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 * Atom decay  || Absorbing photon energy  || Releasing photon energy 
 * Equilibrium || $$hf = hf_o + \frac{1}{2} m v^2$$ || $$nhf=mvr 2 \pi$$
 * v || $$\sqrt{\frac{2}{m}(hf-hf_o)}=\sqrt{\frac{2}{m}(nf_o)}$$|| $$\frac{1}{2 \pi} \frac{nhf}{mr}$$
 * r || || $$\frac{1}{2 \pi} \frac{nhf}{mv}$$
 * n || || $$2 \pi \frac{mv}{hf}$$
 * }
 * r || || $$\frac{1}{2 \pi} \frac{nhf}{mv}$$
 * n || || $$2 \pi \frac{mv}{hf}$$
 * }
 * n || || $$2 \pi \frac{mv}{hf}$$
 * }
 * }