# Effect of the Induced Magnetic Field

I'd like to apologies in advance for the horrible diagram, my question is regarding the following situation:

Consider a circular loop of wire placed within an external magnetic field; this field varies with time and is given by the following expression: $$\vec{B} = B_{0}f(t) \hat{k}$$ Given that the circle has a radius $$r$$ find an expression for the induced emf in the loop as a function of time.

My question is regarding the usage of Faraday's law, since there is a changing magnetic field, an electric current will be induced within the circle, this current however also induces its own magnetic field which opposes the change in the external field.

Most applications of Faraday's law that I have seen do not factor in this induced field with computing the total magnetic flux through the loop, in fact they neglect it. Why exactly do we neglect this induced field when computing the flux through the loop?

My Further question is that say we were trying to compute the total force on the loop as a consequence of the changing magnetic field, do we factor the induced field into such a calculation?