Electric Generators and Faraday's Law

[Violagirl]

Homework Statement

When a generator turns at 60 Hz, the amplitude of the induced EMF is 50 V. What is its amplitude when it turns at 180 Hz if the magnetic field remains the same?

Homework Equations

ω = 2∏f

ε = ε₀sin ωt

The Attempt at a Solution

If f = 180 Hz,

ω = 2∏(180 Hz)

ω = 1131 m/s

To find ε₀ at 180 Hz:

ε/sin ωt = ε₀

From this I get:

(50 V) / sin(1131 m/s)

ε₀ = 64.3 V

However my book says that the answer should be 150 V and I'm not sure what I did wrong with it...

 

[physics&math]

50V is ε0.
ε0 = NABω. NAB doesn't change.

Solve for NAB and use that value to solve for the new ε0.

 

[Violagirl]

Thank you so much! Figured it out!