Download Physics 1B: Electrostatics, Electric Fields, Potentials, Current, Resistance, Capacitance and more Study notes Physics in PDF only on Docsity! Formulas for Physics 1B Prof. David Kleinfeld Winter 2007 Quiz 1 – Electrostatics The force on charge q1from charge q2 is F12 = ke q1q2 r12 2 r̂12 , where the direction vector r̂12 points from q2 to q1 and the proportionality constant is ke = 8.99x109 Nm2/C2. Note that the permittivity of free space is ε0 ≡ 1 4πke = 8.85x10-12 C2/(Nm2) = 8.85x10-12 A2s4/(kg m3). Note that the unit of elemental electronic change is e- = -1.60x10-19C. We note the Taylor’s expansion 1+ x( )n = 1 + nx + ⋅ ⋅ ⋅ ⋅ , which is useful when nx << 1. For example, 1 (r + d)2 = 1 r2 1+ d r ⎛ ⎝⎜ ⎞ ⎠⎟ −2 = 1 r2 1 − 2 d r + ⋅ ⋅ ⋅ ⎛ ⎝⎜ ⎞ ⎠⎟ 1 r2 − 2 d r3 for d << r. The force on a test charge q0 induced by an electric field, denoted E , is F = q0 E . Quiz 2 – Fields and Potentials The electric flux through a surface is Φe ≡ E⊥ΔA All Surfaces ∑ = EΔAcosθ All Surfaces ∑ , where ΔA⊥ = ΔA cosθ is the component of the area whose normal lies parallel to the electric field; θ is the angle between the direction of the electric field and that of the normal to the surface. Gauss’ Law relates the total flux through a closed surface to the total net charge enclosed by the surface, i.e., Φe = 4 π ke QTotal. The electric field produced by a point charge q at the origin, i.e., r = 0, is E = ke q r2 r̂ where r̂ is the radius vector in spherical coordinates. The electric field produced by a line charge, with charge per unit length λ, is E = 2ke λ r r̂ , where the line is defined to lie along the ẑ axis and r̂ is the radius vector in cylindrical coordinates. Formulas for Physics 1B Prof. David Kleinfeld Winter 2007 The electric field produced by a surface charge, with charge per unit area σ, is E = 2πkeσ n̂ , where the surface lies in the x̂-ŷ plane and ẑ corresponds to the normal to the x̂-ŷ plane in Cartesian coordinates. Work-Energy Theorem: W = ΔKE + ΔPE Electric potential: ΔV = -E Δx cos θ, where ΔV = ΔPE Q V = ke q r a distance r away from a point charge q. Quiz 3 – Current, Resistance and Capacitance Current: I = ΔQ Δt or I = n e vD A where n is the density of charge carriers, vD is the drift velocity and A is the cross-section of the wire. Capacitance: Q = C ΔV where C = κ 4πke A d for parallel plates and κ is the dielectric constant I = C ΔV Δt Energy Stored = 1 2 Q ΔV = 1 2 C ΔV( )2 = 1 2C Q2 Resistance: V = I R where R = ρ L A ; ρ is the resistivity in Ohm-m and L is the length of the wire. Power Dissipated = IV = I2R = V2/R Kirchoff’s Laws: 1) Sum of voltage drops around any loop is zero, i.e., gains = losses 2) Sum of current flow at a node is zero, i.e., total current in = total current out A resistor/capacitor pair charges with a characteristic time, denoted t, that is given by the product of the resistance and membrane, i.e., τ = RC. Quiz 4 –Magnetostatics (Electrostatics in the Fast Lane) The force on a test charge q0 induced by an electric field, denoted E , and a magnetic field, denoted B, is F = q0 E + q0 v × B . The cross product v × B points normal to the plane defined by v and B , and has magnitude | v || B |sinθ and a direction that is found from the “right hand rule”.
