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Unformatted text preview: Electricity and Magnetism Coulomb’s Law: F = k*(q 1 q 2 )/r 2 F units: Newtons • A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at its center • If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell Electric Fields : E field = F /q =k(q)/r 2 (units: N/C) (for a point charge) • The direction of E is the direction of the force on a (+) charge • E field lines extend away from (+) charges and toward (-) charges • F =q E : Force, F, same direction as E if q is (+), opposite if q is (-) Gauss’s Law : • Gauss’s Law relates the E fields at points on a closed Gaussian surface and the net charge enclosed by that surface, integral for Gaussian surface can = 0 if net enclosed charge = 0, Gaussian surface does not have to enclose charges then § E*dA=0 Φ electric = § E*dA = § Ecos θ dA (Electric Flux thru a Gaussian Field) ((N*m 2) /C) • E field and Area vector point in same direction, parallel • The electrical flux thru a Gaussian surface is proportional to the net # of E field lines passing thru that surface § E * dA =q/ε EA=q enc / ε • If an excess charge is placed on an isolated conductor, that amount of charge will move entirely to the surface of the conductor. None of the excess charge will be found with in the body of the conductor Electric Potential : U = electric potential energy W=work done by electrostatic force ΔU = U f-U i = -W f = -∫F* d s F=q *E field ΔU=-q *∫E* d s Electric Potential Difference : ΔV= V f-V i = -W/q = ΔU/q 0 = -∫E* d s V=k(q)/r U=qV *note: V is scalar, E is vector Capacitance : q=CV (C: Farad) C=q/V=ε (A/d) (for parallel plate capacitor), C=2 πε ℓ/ln(b/a) (cylindrical capacitor), C = 4 πε ab/(b-a), where a-inner radius, b-outer radius Series: Parallel: V T = V 1 + V 2 + V 3 V T = V 1 = V 2 = V 3 q T = q 1...
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- Spring '08
- Magnetic Field, Electric charge, specific case, Surface area sphere