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## Homework Statement

The current in a solenoid (you may treat it as a long solenoid of length 2.0 m, turns, and radius 0.5 m) is decreasing at a rate of 1.7 A/s.

What is the EMF at a point .35m inside the solenoid?

## Homework Equations

- B=N(mu_0*I)/(2a)
- where B=magnetic field, N=turns per length, I=current, and a=radius

- Epsilon=d(phi)/dt
- where Epsilon=EMF, phi=magnetic flux, and t=time

- Phi=int(B dot dA)
- where A=cross sectional area and you take the dot product of the two vectors

- A=pi*r^2
- where r=new radius (.35m inside the solenoid)

## The Attempt at a Solution

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- I have tried saying that Epsilon = -N(BA/t) and then substituting (mu_0*I)/2a in for B and pi*r^2 in for A so that Epsilon= -N*((mu_0*I)/2a)*(pi*r^2)*(1/t) and then pulling out I/t as my decreasing current over time.
- I have also tried when r=a and they are both .5m and when they are both .15m
- I have also tried finding the flux at some random current (11A) and then finding the flux after one second due to the decreasing current and then plugging those values in to my Epsilon=d(phi)/dt equation