Notes for the Physics GRE - Harvard University Department of Physics

Given two parallel wires separated by a distance a, each carrying a current I i ,the force per unit length f between the wires isf = µ 0I 1 I 22πa . (87)If the currents are in the same direction, the force is attractive. If they are inopposite directions, the force is repulsive.Ampere’s Law: ∮⃗B · d⃗s = µ 0 I(+µ 0 I d ). (88)Here, the term in parentheses is Maxwell’s correction term, and I d = ɛ 0dΦ Edt .The loop around which we are integrating should be taken to encircle thewire/conductor of interest. For an infinitely long solenoid, this gives an interiormagnetic field of,B = µ 0 In (89)where n = N/l is the number of turns per unit length. Outside the infinitelylong solenoid, the magnetic field vanishes.For a long, current-carrying wire of radius R,B = µ 0 I 12πr , r ≥ R= µ 0 Ir 12πR, r < R.2Magnetic flux through a surface:∫Φ B =For uniform ⃗ B, planar ⃗ A,S(90)⃗B · ⃗A. (91)Φ B = BA cos(θ). (92)For a closed surface, Gauss’s law for magnetism:∫Φ B = ⃗B · ⃗A = 0. (93)SThis is assuming that there are no magnetic monopoles in nature, which shouldbe your working assumption for the pGRE.Given a magnetic field B 0 and a material, the magnetic field in the materialis:B = B 0 + B m = B 0 + µ 0 M = µ 0 (H + M), (94)where H is the magnetic field strength and M is the magnetization of thesubstance. For para/dia-magnetic materials,M = χH, (95)13