Max EMF in a Model AC Generator Coil

[mydoghenry]

Homework Statement

In a model ac generator, a 500 turn rectangular coil, 8.0 cm by 20 cm, rotates at 120 rev/min in a uniform magnetic field of 0.60 T.

(a) What is the maximum emf induced in the coil?
(b) What is the instantaneous value of the emf in the coil at t = (∏/32)s? Assume that the emf is zero at t = 0.
(c) What is the smallest value of t for which the emf will have its maximum value?

Homework Equations

εmax=NBAω
ε=εmaxsinωt

The Attempt at a Solution

I easily understand part a and b (below):
(a)
Area=0.08x0.20=0.016 m2
120rev/min = 12.56 rad/s

εmax=NBAω
εmax=500(0.60)(0.016)ω
εmax=60.28V

(b)
ε=εmaxsinωt
ε=60.28sin(12.56∏/32)
ε=56.87V

(c)
Part c is where I am totally confused. We did this problem in class, so I will show you what my teacher came up with and explain why I don't understand.

ε=εmaxsinωt
ωt=∏/2 --> ε=εmax
12.56t=∏/2
t=∏/2(12.56)=0.125 s

I do not understand where/how my teacher came up with ωt=∏/2. Why are we dividing pi by 2? And how do we know this is equal to ωt? Are we just supposed to know this equation? Is it a common physics rule? I want to know the "why" behind it and not just memorize that equation so I can apply it to other situations. For instance, what if we're asked what the largest value of t for which the emf will have it's maximum value?" Then it wouldn't still be pi over 2?

I have a test Thursday and have been wracking my brain trying to figure out why or how he came up with part c. I would greatly appreciate any and all help. Thank you so much! :!)

 

[tiny-tim]

welcome to pf!

hi mydoghenry!

ε=εmaxsinωt
ωt=∏/2 --> ε=εmaxsinωt
…
I do not understand where/how my teacher came up with ωt=∏/2.

the maximum value of sin (= 1) is when the angle is π/2

 

[mydoghenry]

Thank you so very, very much. It makes sense now. I must have missed the day in class when we learned ∏/2 is the radian form of 90°.

Do you think there's any other way for that question to be asked? For instance, What is the smallest value of t for which the emf will have its minimum value? In this case would it be sin180 (aka sin∏) which I guess is zero. So, maybe there's only one way he'd ask this question.

 

[tiny-tim]

So, maybe there's only one way he'd ask this question.

yes …

he's really not trying to trick you! ​