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Magnetic force on a moving charge r v r F = qv × B Magnetic force on a current-carrying wire r r r F = LI × B v µ0 qvv × rˆ Magnetic field created by a moving charge B = 4π r 2 r v µ0 I dl × rˆ B = Biot-Savart field created by a wire carrying a current 4π r 2 v µ0 I Biot-Savart field created by a straight wire B = 2πr Force between parallel wires F= µ0 I ' I L 2πr r r ∫ B ⋅ dl =µ0 I thru Ampere’s law Loop Field inside a coil: Faraday’s Law Inductance B = µ0nI = µ0 Field inside a toroidal solenoid B= µ0 NI 2πr r r dΦ B ε = ∫ E ⋅ dl = − dt Loop ε = −L Magnetic energy N I L dI Φ where L = B dt I 1 2 B2 U = LI and u = 2 2 µ0 . For a toroidal solenoid: µ0 N 2 A L= 2πr Units and constants: Electricity: ε 0 = 8.854 × 10−12 C2 /N.m2 and 1 4πε 0 = 9.0 × 109 N.m2 / C2 e = 1.602 × 10−19 C [Charge]=Coulomb=C [Electric Force]=Newton=N [Electric Field]=[Force]/[Charge]=N/C=[Voltage]/[distance]=Volt/meter= V/m [Energy]=Newton.meter=Joule=J [Voltage]=[Energy]/[Charge]=J/C=Volt=V [Capacitance] = [Charge]/[Voltage]=Coulomb/Volt=C/V=Farad=F [Current] = [Charge]/[time]=Coulomb/sec.=C/s=Amp=A [Resistance] = [Voltage]/[Current]=Volt/Amp= Ohm=Ω Magnetism: µ0 = 4π × 10−7 Tm/A and µ0 = 10−7 T.m / A 4π [Magnetic Field]=[Newton/Ampere.meter] =N/Am=Tesla=T [Inductance]= [L] = [Tesla meter2]/[Amperes] = [Henry]=H