Equation sheet

# Equation sheet - Constants Ke = 9.0x109N-m2/C2 0= 1(4Ke =...

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Constants: K e = 9.0x10 9 N-m 2 /C 2 ε 0 = 1/(4πK e ) = 8.85x10 -12 C 2 /N-m 2 1ev=1.60x10 -19 C-V=1.60x10 -19 J 1kWh=3.60x10 5 J m electron =9.109x10 -31 kg m proton =1.672x10 -27 kg q electron =-1.60219x10 -19 C μ o =4π*10 -7 Tm/A Field lines: positive negative F=K e |q 1 ||q 2 |/r 2 = qE E= K e |q|/r 2 =Q inside /(ε o A) (E=electric field (N/C)) ΦE = EAcosθ = Q inside 0 =EA (ΦE=electric flux (N-m 2 /C) ΔPE = -W AB = -qEd=VΔQ ΔV = ΔPE/q = ΔV o /κ (ΔV= electric potential (N/ C=V/M)( κ=dielectric constant) V=K e q/r=IR=Ed PE = q 2 V 1 =K e q 1 q 2 /r W= -q(V b -V a ) C= -Q/ΔV= κ*ε 0 A/D= κC o (C=capacitance (F)) 0 in this case is permittivity of free space) Q=CV σ=Q/A (σ=charge density) E c = ½QΔV=Q 2 /(2C) =½ CV 2 For parallel capacitors: Q=Q 1 +Q 2 V 1 =V 2 C eq =C 1 +C 2 +C 3 +… Q=C eq ΔV For series capacitors: Q 1 =Q 2 ΔV=ΔV 1 +ΔV 2 =Q/C 1 +Q/C 2 =Q/C eq 1/C eq =1/C 1 +1/C 2 +1/C 3 +… I=ΔQ/Δt= nqV d A (I=current (A)) ΔQ=(nAV d Δt)q (n=number of electrons/volume) R=V/I =ρL/A ρ=ρ o (1+a(T-T 0 )) (a=temp. coefficient of resistivity) R=R o (1+a(T-T 0 )) P=IV=ΔQΔV/ΔT=I 2 R=V 2 /R (P=power (watt)) Resistors in series: I 1 =I 2 R eq =R 1 +R 2 +… ΔV=IR eq Resistors in parallel: ΔV 2 =ΔV 1 I=I 1 +I 2 1/R eq =1/R 1 +1/R 2 +… I=ΔV/R eq Kirchoff 1: I 1 =I 2 +I 3 Kirchoff 2: Must gain as much energy as it loses in closed loop E 1 =IR 1 +IR 2 (draw pic in notes) RC Circuits For charging: q capacitor =Q(1-e -t/RC ) RC=τ=time for q to go 0 63.2%Q V capacitor =Q/C (1-e -t/RC )=V(1-e -t/RC ) V resistor =V-V c I=V/R (e -t/RC ) For discharge: q c =Qe -t/RC F=qvBsinθ (B=magnetic field (T)) F max =qvB Thumb=motion, pointer=field, others=force r=mv/(qB) F wiretot =BILsinθ τ=BIANsinθ=μBsinθ (τ=torque) μ=IAN (μ=magnetic moment (Am 2 )) B= μ 0 I/(2πr) B 2 = μ 0 I 2 /(2πd) F 2 1 /l= μ 0 I 1 I 2 /(2πd) B center = μ 0 I/(2R) B centersolenoid = μ 0 NI/L I 1 I 2 I 3 I towards you I away

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μ o =4π*10 -7 Tm/A Thumb=motion, pointer=field, others=force (opp. For negative charges) Thumb=dir. Of current, fingers curled=dir. Of magnetic field F=qvBsinθ (B=magnetic field (T)) F max =qvB r=mv/(qB) F wiretot =BILsinθ τ=BIANsinθ=μBsinθ (τ=torque) μ=IAN (μ=magnetic moment (Am 2 )) B= μ 0 I/(2πr) B
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