There seems to be a pretty standard formula, that if a wire of length ell carrying current I is immersed in a magnetic field B, then the magnitude of the magnetic force is F_B = I ell B sinθ, where the direction of F_B is the direction of ell times B (determined using right-hand rule). But, these properties can all be summarized into the equation dB = frac mu_04 pi fracId ell times rr². I understand the first equation, but don't get the second one. How would I even read this equation or apply it? Do I have to integrate first? How would this work?