# Find the maximum induced emf in the large coil solenoid

1. Jul 30, 2007

### kiwikahuna

1. The problem statement, all variables and given/known data
Given: u_0 = 1.25664e-6
A 2 m long large coil with a radius of 14.6 cm and 320 turns surrounds a 4.2 m long solenoid with a radius of 4.6 cm and 7700 turns. The current in the solenoid changes as I = I_0 sin (2pi*f*t) where I_0= 30 A and f=60 Hz.Inside solenoid has 7700turns and outside coil has 320 turns. The equation for the emf is E = E_0sin(omega*t). There is also a resistor on the smaller coil that is 25 ohms. Find the maximum induced emf in the large coil. Answer in units of V.

2. Relevant equations
Magnetic field = B = u_0 * I / (2*pi*r)
Flux = BA

3. The attempt at a solution
I found the magnetic field of the solenoid (0.069115sin(120*pi*t)) and the area (0.006648). I then multipled BA to find the flux which is (0.000459 sin(120*pi*t))

Then I found the magnetic field of the outer coil ((0.006032sin(120*pi*t)) and the area to be 0.066966.
The magnetic flux is BA = (0.000404sin(120*pi*t))

Now I am truly stuck because I've no clue where to go from here. Please help! Many thanks.

2. Jul 31, 2007

### Matthaeus_

I think Ohm's Law and Faraday's Law would help:

$$\displaystyle V = iR$$

$$\displaystyle \oint\vec{E}\cdot d\vec{l} = \mathcal{E}_{ind} = -\frac{d\Phi_B}{dt}$$

3. Jul 31, 2007

### kiwikahuna

Hmm...I'm still lost. Could you perhaps clarify what you mean and how those two equations would relate to each other.

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