1. The problem statement, all variables and given/known data Griffith ( Introduction to electrodynamics , 3 ed.) says in Problem 7.9: An infinite number of different surfaces can be fit to a given boundary line, and yet, in defining the magnetic flux through a loop, Φ = ∫B.da, I never specified the particular surface to be used. Justify this apparent oversight. 2. Relevant equations 3. The attempt at a solution I have always taken that surface which is perpendicular to the B and contains the loop as its boundary. I guess that Griffith doesn't define the surface because what we want to calculate is ε = - dΦ/dt and dΦ/dt doesn't change w.r.t. surface. But ,I don' t know in which direction should I think? In page no.296 , Griffith says Apart from its delightful simplicity, it has the virtue of applying to non- rectangular loops moving in arbitrary directions through non- uniform magnetic fields; in fact, the loop need not even maintain a fixed shape. But, won't calculating Φ for non- rectangular loops and non uniform magnetic fields itself be hard?