Induced magnetic flux through a coil

[Gnarlywhale]

Homework Statement

A circular conducting coil with N=100 turns and radius "r" is oriented in the xy plane. The leads of the coil are connected to a circuit with resistance "R." A time varying external magnetic flux density "B" is applied along the z-axis.

What is the total magnetic flux through the coil as a function of time?

Homework Equations

Φ = BA

The Attempt at a Solution

Φt = Φb - Φi
Φt = BA - Φi

(where Φt is the total magnetic flux through the coil, Φb is the externally applied magnetic flux and Φi is flux induced by lenz's law).

I am aware that there is an induced magnetic flux but cannot figure out how to determine it from the external magnetic flux. Is there just some equation I can't seem to locate?

 

[ideasrule]

Are you sure that's the whole problem? You can't determine the induced magnetic flux unless you know how B varies with time, because induced EMF is equal to negative the change the magnetic flux.

 

[Gnarlywhale]

They do give you a formula for B,

B = Bi(1 - 3(t/ti)^2 + (t/ti)^3)

Everything is still left as a variable.

So from this then, E = -N(dΦ/dt) = -100*Bi(1 - 3(t/ti)^2 + (t/ti)^3) ?

And then how do I get flux from this emf?