Question about magnetism/induced emf in small coil

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The discussion centers on calculating the induced electromotive force (emf) in a small coil placed within a solenoid. The solenoid has specific dimensions and carries a current that is switched off, leading to a change in magnetic flux. The magnetic flux through the small coil is initially calculated to be 14.4 x 10^-6 Weber, and when the current is turned off, the flux decreases to zero. The change in magnetic flux (delta Φ) is therefore 14.4 x 10^-6 Wb. The induced emf can be determined using the formula, considering the time interval of 25 ms for the current switch-off.
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Homework Statement


A solenoid with a length of 25.0 cm, radius 1.60 cm and 5500 turns carries a current of 1.50 A. A small coil of radius 1.05 cm and 130 turns is placed at the center of the solenoid with its axis in the same direction as that of the solenoid. A 470 ohms resistor is connected to the ends of the small coil. The current in the solenoid is switched off within 25 ms.

Determine the magnitude of the induced emf in the small coil.

Homework Equations



Induced EMF= -N delta \Phi / delta t

The Attempt at a Solution



The main problem I am having is figuring out the change of the magnetic flux. I figured out the magnetic flux through the small coil at 14.4 x10^-6 WB (from the equation magnetic flux=BA cos theta) but I don't know what it changes to or from.
 
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Since the current in the solenoid is switched off, it no longer produces a magnetic field. So the flux changes to 0 over the course of 25 ms.
 
so for delta \Phi it would be (14.4x10^-6)-(0)?
 

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