PHY132 Formulae Final

University Physics with Modern Physics with Mastering Physics (11th Edition)

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Formulae: Electric Charge Q [C] : Q e = 1.602×10 –19 C = e, Q p = + e, m e = 9.11×10 –31 kg, m p = 1.67×10 –27 kg Current: I dQ/dt Unit: A (mpère) C/s I = qn q Av drift ; v drift E q is the charge of the mobile charges, n q their density, A the wire’s cross section, E the local electric field strength Coulomb Force: Force between two point-charges Q 1 and Q 2 separated by distance r 12 Force exerted by Q 1 on Q 2 , r 12 points from 1 to 2 92 2 1 2 2 2 12 1 on 2 0 2 01 2 0 11 , 8.998 10 Nm /C , 8.85 10 C /(Nm ) 44 QQ r ε πε == × = × Fr ± Electric Field (Vector Field!): E F E / q Force-per-unit-test-charge: N/C Field of a point charge Q Field outside a spherically symmetric charge Q ( r>R ) 2 0 force on charge : 1 , 4 q q Q q r =⇒ = Er FE ± Field of a line charge λ =Q/L Field outside ( r n >R ) a cylindrically symmetric charge λ l l 0 1 ( is unit vector normal to the line) 2 n n r λ = r Field of a planar charge σ =Q/A ; for infinite plane, or close compared to the size of the plane… l l 0 ( is unit vector normal to the plane) 2 σ = A EA Field of a uniformly charged ring, radius R , on a line ring and through the center ( x -axis!) 22 3 2 3 2 00 1 4( ) 2 ( ) QR xR ++ xx E Field inside a conductor E =0 when no EMF is present: the mobile charges rearrange them- selves to cancel an external field ( E 0 when an EMF is present!) Energy density u (energy/unit volume) of electric field E : 2 0 2 uE = Gauss’ Law for E: 0 closed surface Flux enclosed E Q d Φ≡ = v Choose the Gaussian surface to match the symmetry of charge distribution and E -field! Magnetic Force: F B = q v×B d F B = I d l×B Force on a charge q , moving with velocity v in magnetic field B Force on a wire of length d l carrying current I , in magnetic field B Force between two parallel wires of length l , car- rying currents I 1 and I 2 , separation distance d 7 012 0 ,4 1 0 T m 2 II F ld / A µ µπ π =≡ × Magnetic Field (Vector Field!): Unit: Force per unit current×length: T(esla) N /(A·m) Field B at position r from a charge q moving with velocity v (Biot-Savart Law) 0 7 2 0 force: () , 41 0 T m / A 4 B q q r = × ≡× Fv B Br v r ± Field d B at position r from a short wire segment length d l , carrying current I (Biot-Savart Law) 0 2 ( ) , force: 4 B I dd d I r d = ×⇒ l r F l B ± Field of a long straight cylindrical wire of radius R , carrying current I 2 (direction: tangential to ;() circles centered on wire) r Br R rR ππ ≥= ≤=
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PHY132 Formulae Final - Electric Charge Q [C]: Current: I...

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