## Formulas 1

 Electric field and potential Coulomb's law: F12 = (keq1q2/r122) (r12/r12). Electrostatic field of a point charge: E = (keq/r2) (r/r). Gauss' law: Φe(through closed surface) = Qinside/ε0. Electrostatic potential energy: ∆U = UB - UA = -q ΣAB E∙∆r. Electrostatic potential difference: ∆V = ∆U/q The potential of a point charge: V(r) = kq/r  (convention:  V = 0 at infinity.) Field and potential: Ex = -∆V/∆x, Ey = -∆V/∆y, Ez = -∆V/∆z Capacitors Capacitance: C = Q/V Parallel plate capacitor: C = εA/d Energy stored in a capacitor: U = ½(Q2/C) = ½CV2 Capacitors in series 1/C = (1/C1) + (1/C2) + (1/C3) Parallel capacitors: C = C1 + C2 + C3 Currents and circuits Current: I = ∆Qnet/∆t = j∙A,  j = current density Resistance: R = ∆V/I Resistance of a straight wire: R = ρL/A Power: P = I∆V = I2R = (∆V)2/R Resistors in series: R = R1 + R2 + R3 Parallel Resistors: 1/R = (1/R1) + (1/R2) + (1/R3) RC circuits time constant: τ = RC Magnetostatics Magnetic force on a moving charge: F = qv × B Magnetic force on a long straight wire: F = IL × B Charged particle in a magnetic field: r = mv/(qB) The magnetic field of a long straight wire: B = μ0I/(2πr) The magnetic field inside a solenoid: B = μ0nI Current loops Magnetic moment: μ = IAn Torque: τ = μ × B,  τ = μB sinθ Potential energy: Uμ = -μB cosθ