Calculating EMF Induced by a Moving Wire in a Magnetic Field

[Sir_Pogo]

Can i get some help with this homework problem??
A physicist wraps a long copper wire around a toilet paper roll and places the roll in a uniform magnetic field. The axis of the roll is aligned with the field. The radius of the roll is r = 6 cm and the strength of the field is B = 0.1 T. If the physicist pulls the wire at v = 78 cm/s, what is the magnitude of the EMF induced in the wire?
Thanks in advance.

 

[OlderDan]

Look at the equation for induced emf related to the flux through a coil of N turns. What is changing when the wire is being pulled? The wire is unwinding from the roll.

 

[Sir_Pogo]

im using dBda/dt and da/ta= .5*r*ds/dt where ds/ts is the velocity
im taking that time the magnetic field.
also i am watchin my units.
so B*.5*r*v=emf? what's wrong its not right tho?

 

[OlderDan]

im using dBda/dt and da/ta= .5*r*ds/dt where ds/ts is the velocity
im taking that time the magnetic field.
also i am watchin my units.
so B*.5*r*v=emf? what's wrong its not right tho?

I don't understand your first equation. Is d the diameter in one place and derivative in another? I think you need to be a bit creative with this one. Usually we take N to be a constant and write

ε = -N[dΦ/dt] = -N[d(BA)/dt]

But in this problem, B and A are constant and effectively N is changing, so

ε = -[d(NAB)/dt)] = = -BA[dN/dt]

How is N related to v?