Electromagnetism, Study notes of Electromagnetism and Electromagnetic Fields Theory

Download Electromagnetism and more Study notes Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity! 1 Electromagnetism General comments: the GRE is in SI units, so for those who took 8.022, make sure to pay attention to where the epsilons and mus go. (And thus the slightly different form of Maxwell’s Equations.) Also, on one of the practice tests I looked at, they asked about which if Maxwell’s equa- tions would need to be modified to account for magnetic monopoles. Work: W q0 has units of volts. Volt = Joules/Coulomb. 1.1 Electricity k = 1 4πε0 [Nm2C−2], ε0 is permittivity of free space F = k q1q2 d2 Force between two charges F = q1E Force on charge in field E = 4πkQ A Uniform electric field between two charged parallel plates, each of area A −→ E = k q−→r r2 −→r in direction + → -. Electric field of single charge. W q = Ed Electric potential V = IR Ohm’s P = VI = I2R Power R = ρ l A Resistivity Rtot = R1 + R2 + ... Resistors in series 1 Rtot = 1 R1 + 1 R2 + ... Resistors in parallel 1.2 Magnetism ~F = ~Eq + ~vq × ~B Lorentz Force Law ~F = I~l +× ~B Force on current carrying conductor B = Φ A Magnetic induction, Φ=magnetic flux R = mv Bq Radius of curvature of moving charge in magnetic field −→ B = µ0 4π q−→v ×br r2 Magnetic field of moving charge 1 ∮ B · dl = µ0I Ampere’s law, use for calculating current 1.3 Capacitors C = Q V = ε0 A d Capacitance, Q = charge on either plate. [farads] UC = 1 2 CV 2 Energy of Capacitor V = Q ε0A d Capacitors in series (or multiple different dielectrics): C = 1“ 1 C1 ” + “ 1 C2 ” Charging: q = (Cε) ( 1− e−t/RC ) Discharging: q = (Cε) ( e−t/RC ) 1.3.1 Undriven RL Circuit: VR + VL = RI + LdI dt = 0 I(t) = I0e −Rt/L RC Circuit: V (t) = V0e −t/RC 1.3.2 Driven RLC Circuit V (t) = Vf︸︷︷︸ forced response +AeS1t +BeS2t︸ ︷︷ ︸ natural response Where S1,2 = −α± √ α2 − ω2 0 α = 1 2RC , ω0 = 1√ LC . 1.4 Maxwell’s Equations Gauss’s Law ~∇ · ~E = ρ ε0 Gauss’s law for magnetism ~∇ · ~B = 0 Faraday’s law ~∇× ~E = −∂ ~B ∂t Ampere’s Law ~∇× ~B = µ0 ~J + µ0ε0 ∂ ~E ∂t NOTE: ~J is the total current density. 1.5 Magnetic and electric fields in matter ε = ε0εr for media other than free space, where εr = relative permitivity of the media. SIMILAR FOR MAGNETS? 2