# Maximum induced emf with 2 Solenoids

## Homework Statement

A 3 m long large coil with a radius of 15.7 cm and 130 turns surrounds a 7.2 m long solenoid with a radius of 5.7 cm and 4700 turns. The current in the solenoid changes as $$I=I_0 sin (2\pi f t)$$ where I0= 30 A and f=60 Hz.Inside solenoid has 4700 turns and outside coil has 130 turns. The equation for the emf is $$E= E_0 sin \omega*t$$ .There is also a resistor on the smaller coil that is 34 ohms. Find the maximum induced emf in the large coil. Answer in units of V.

http://img194.imageshack.us/img194/5624/87290481.jpg [Broken]

## Homework Equations

$$emf = -N\frac{d\phi}{dt}$$

Magnetic field of solenoid

$\mu_0IN/L$

## The Attempt at a Solution

I will show my work done till now.If there is any mistake i made or step i forgot please tell me.

First i have to find the magnetic field of the inner solenoid.

Then i have to calculate the flux of the inner solenoid.

After that i have to use the magnetic field of inner solenoid to find the flux of outer solenoid.

Now i have to find the change in flux but the question here is , Do i have to subtract the inner from the outer or the opposite ???

Is is $$\phi$$Outer - $$\phi$$Inner ???

Or $$\phi$$Inner - $$\phi$$Outer ???

Now i know that i have to derive the flux change with respect to time but another question is here , shall i subtract the two fluxe first then derive the change or shall i derive them before subtraction ??? ( I think that i will get the same answer whatever choice i select )

After i get the answer ( which i hope to get it very soon ) i will just multiply the whole thing i mean the time rate of change of that flux with the number of turns for the outer solenoid .

Please check my steps & tell me if i did something wrong.

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Please any one who can point me to the right direction ...

there is no need to substract inner or outer flux....
after u found out the flux developed by inner solenoid,
find the flux associated with the outer solenoid and then the time derivative will directly yield the induced emf in large coil...

emf= -N d(flux)/dt
the flux is one associated with the coil... no need of substraction ...

thanks for response

hmmm.. ok there is no need to substract one from another,

how do i find the flux associated with the outer one ?

Do i have to use the inner magnetic field to find the outer flux ??

Or

Do i have to use the inner flux to find the outer flux and how ??

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