Clarification on induced current/Bfields for solenoids

[aimslin22]

Homework Statement

I'm working on induced currents/b-fields from Lenz's Laws and two different problems use the same equation but one has an extra variable and I don't know when to add this equation.

Problem 1:
In a physics laboratory experiment, a coil with 180 turns enclosing an area of 11.6cm^2 is rotated during the time interval 3.10×10−2s from a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is 5.00×10−5T. What is the total magnitude of the magnetic flux ( Phi_initial) through the coil before it is rotated?

Problem 1:
Phi = BAcostheta
This relation is just for one loop, and when we are calculating the effect of all the loops in the coil we must remember to multiply by N, the total number of loops. In other words Phi_initial = N*Phi_1.

^Now this completely makes sense to me, but I just did another problem:

Problem 2:
A 100-turn 8 cm diameter coil is made of 0.5 mm diameter copper wire. A magnetic field is perpendicular to the coil. At what rate must B increase to induce a 2 A current in the coil?

I did this problem perfectly, but I I'm off by a factor of 100 because I divide my flux by 100 to account for the numbers of turns.

My question is: why do I need to account for the turns in one problem and not another? ie. In the future, how will I know what to do?

Thank you!

 

[UVW]

Remember, in Problem 2, you first found the necessary flux. When you divide by the number of turns, you're finding the necessary flux per turn. You just want the flux, though, so it makes sense to not divide.

In the future, it usually works best to think about what's happening physically. For example, in the first problem, it makes sense that the flux through a coil with 100 loops ought to be 100 times more than the flux through just one loop, so it's good that you multiplied.

Most of the time, you are going to want to calculate things for the entire coil, not just for one loop.

 

[aimslin22]

I see. Thank you!