PHY131 - Formulas

PHY131 - Formulas - Ch. 21: Coulombs Law: F=kq1q2r2, k=140...

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Ch. 21: Coulomb’s Law: = , = F kq1q2r2 k 14πϵ0 = force between two point charges (in a vacuum). Electric field : = = = E F0q0 F0 Eq0 ma Electric field of a point charge : = E qr4πϵ0r2 REMEMBER: = r rr Electric field of a ring of charge : = = + E Exi Qx4πϵ0x2 a232i (for a ring with symmetry on x axis, centered in yz plane). Field of a finite line of charge: = + E Q4πϵ0xx2 a2i With charge density λ, λ=Q/2a: = + E λ2πϵ0xx2a2 1i thus = E λ2πϵ0r for infinite line of charge Field for finite, uniformly charged disk : = - Ex σx2ϵ01 + 1R2x2 1 = E σ2ϵ0 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) τ=pEsin -> 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: Φe = ∫ E cosφ dA = E dA = E . d A = Q encl o = Gauss’s Law Single pt charge, E = (1/4πε o )(q/r 2 ) Charge on surface of conducting sphere, E = (1/4πε o )(q/r 2 ) Inside sphere = 0 Infinite wire, E = (1/2πε o )( λ /r) Infinite conducting cylinder, E = (1/2πε o )( λ /r) Inside = 0 Solid insulating sphere, Q distributed uniformly throughout, E = (1/4πε o )(Q/r 2 ) Inside sphere E = (1/4πε o )(Qr/R 3 ) Infinite sheet with uniform charge, E = σ/2ε 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 = (1/4πε o )(qq 0 /r) = (q 0 /4πε o )(q 1 /r 1 + q 2 /r 2 + …) Equi triangle: U = (1/4πε 0 )(1/r)(q 1 q 2 +q 2 q 3 +q 1 q 3 ) V = U/q 0 = (1/4πε o )(q/r) or (q 0 /4πε o )(q 1 /r 1 + q 2 /r 2 + …) V = (1/4πε o ) ∫ (dq/r) Va – Vb = ∫ E d l = ∫E cosφ dl E = -(dV/dx i + dV/dy j + dV/dz k ) V for a point outside a sphere (r away): = V q4πϵ0r V for inf. line charge or charged conducting cyl .: = ( ) V λ2πϵ0ln Rr V in oppositely charged plates (y-axis up is positive): V=Ey, - = → = Va Vb Ed E Vabd (a is top, +plate, b is bottom, -plate) Charge density for above: = σ ϵ0Vabd V for rod of length 2a : = ( + + + - V Q4πϵ02aln a2 x2 aa2 x2 ) a V for point x from center of ring of charge : = + V Q4πϵ0x2 a2 Ch 24 – Capacitance, Dielectrics:
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PHY131 - Formulas - Ch. 21: Coulombs Law: F=kq1q2r2, k=140...

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