Final Formulas

Final Formulas - Ch. 21: Coulombs Law: Electric field:...

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Ch. 21: Coulomb’s Law: = force between two point charges (in a vacuum). Electric field : Electric field of a point charge : REMEMBER: Electric field of a ring of charge : (for a ring with symmetry on x axis, centered in yz plane). Field of a finite line of charge: With charge density , =Q/2a: λ λ thus for infinite line of charge Field for finite, uniformly charged disk : for infinite charged disk For two oppositely charged, infinite sheets, E inside is 2E, outside either sheet is 0. Dipole = pair of pt. charges with equal magnitude, opposite sign p=qd -> p =q d (p = dipole moment) =pEsin -> τ τ = p x E, U=- p*E Potential energy U at its lowest when dipole is in stable equilibrium. U = -pEcos Ch 22 – Gauss’s Law, Eflux: e = E cos dA = E Φ φ dA = E . d A = Q encl / ε o = Gauss’s Law Single pt charge, E = (1/4 πε o )(q/r 2 ) Charge on surface of conducting sphere, E = (1/4 πε o ) (q/r 2 ) Inside sphere = 0 Infinite wire, E = (1/2 πε o )( /r) λ Infinite conducting cylinder, E = (1/2 πε o )( /r) λ Inside = 0 Solid insulating sphere, Q distributed uniformly throughout, E = (1/4 πε o )(Q/r 2 ) Inside sphere E = (1/4 πε o )(Qr/R 3 ) Infinite sheet with uniform charge, E = /2 σ ε o 2 oppositely charged conducting plates, E = / σ ε o Ch 23 – Potential energy, electric potential: W a b = U a - U b =-(U b -U a ) U=Fd=q 0 Ed K b +U b =K a +U a U = (1/4 πε o )(qq 0 /r) = (q 0 /4 πε o )(q 1 /r 1 + q 2 /r 2 + …) Equi triangle: U = (1/4 πε 0 )(1/r)(q 1 q 2 +q 2 q 3 +q 1 q 3 ) V = U/q 0 = (1/4 πε o )(q/r) or (q 0 /4 πε o )(q 1 /r 1 + q 2 /r 2 + …) V = (1/4 πε o ) (dq/r) Va – Vb = E d l = E cos dl φ E = -(dV/dx i + dV/dy j + dV/dz k ) V for a point outside a sphere (r away): V for inf. line charge or charged conducting cyl .: V in oppositely charged plates (y-axis up is positive): V=Ey, (a is top, +plate, b is bottom, -plate) Charge density for above: V for rod of length 2a : V for point x from center of ring of charge : Ch 24 – Capacitance, Dielectrics: C = Q/V ab
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This note was uploaded on 09/17/2008 for the course PHY 131 taught by Professor Fuchs during the Spring '07 term at ASU.

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Final Formulas - Ch. 21: Coulombs Law: Electric field:...

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