What is the Correct Method for Finding Induced EMF in a Coil?

AI Thread Summary
To find the induced EMF in a coil with a diameter of 4.0 cm and 1000 turns, the magnetic field is given as B=(0.30i + 0.50t² k). The induced EMF is calculated using the formula ε=dΦ/dt, where Φ is the magnetic flux defined as Φ=ABcosθ. An attempt at the solution led to ε=0.00129V k, but there was uncertainty about the correctness of the method. It was suggested to first sketch the coil and position the coordinate system accurately to ensure proper calculations. Proper visualization and setup are crucial for accurate results in this problem.
ReidMerrill
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Homework Statement


A 4.0 cm diameter coil (1000 turns) is at rest in the XY plane. The magnetic field in this region of space is given by B=(0.30i + 0.50t2 k) What is the induced EMF in the coil at t=2.0 seconds

Homework Equations


ε=dΦ/dt
Φ=ABcosθ

The Attempt at a Solution


ε=[/B]d/dt( πr2)(0.03i+0.5t2 k) Cosθ
ε=πr2cosθ *0.5*2t k

Using trig I found θ=59° and plugging in the numbers I got ε=0.00129V k

I assume I did something wrong. Is this anywhere close to the proper method?
 
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You need to first sketch the correct diagram! Draw a circle, and position your co-ordinate system inside that circle (the ring) appropriately.
 

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