Ihave an exam tomorrow and just need to know the steps and equations to find the induced current in a coil because of the solenoid. i also someone to explain how to find the direction of the current. just keep it clear and not confusing.

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k