Quick Recap — Forces, Torques & Magnetism

  • Force on a wire: F=BILsinθF = BIL\sin\theta; parallel wires attract (same direction) or repel (opposite), with FL=μ0I1I22πd\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi d} — this defines the ampere.
  • Current loop: magnetic moment m=NIAm = NIA; torque τ=mBsinθ=NBIAsinθ\tau = mB\sin\theta = NBIA\sin\theta.
  • Galvanometer: a small parallel shunt makes an ammeter; a large series resistance makes a voltmeter.
  • Bar magnet: the axial field is twice the equatorial field at the same distance, and both fall off as 1/r31/r^3.
  • Materials: diamagnetic (weakly repelled), paramagnetic (weakly attracted) and ferromagnetic (strongly attracted; they become paramagnetic above the Curie temperature).