- #1
mydoghenry
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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! :!)