# Maximum induced emf with 2 Solenoids

• Fazza3_uae
In summary, the problem involves a large coil and a solenoid with varying current and a resistor. The task is to find the maximum induced emf in the large coil, which can be achieved by finding the flux associated with the solenoid and the outer coil. The magnetic field of the inner solenoid and the flux it creates are used to find the flux of the outer solenoid. The emf is then calculated by taking the time derivative of the flux. There is no need to subtract one flux from the other.
Fazza3_uae

## 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

## 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.

Last edited by a moderator:
Please anyone 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 ??

Last edited:

## 1. What is the maximum induced emf with 2 solenoids?

The maximum induced emf with 2 solenoids depends on the number of turns in each solenoid, the magnetic field strength, and the rate at which the magnetic field changes. It can be calculated using the equation: emf = -N1N2A(dB/dt), where N1 and N2 are the number of turns in each solenoid, A is the cross-sectional area, and dB/dt is the rate of change of the magnetic field.

## 2. How do the number of turns in each solenoid affect the maximum induced emf?

The greater the number of turns in each solenoid, the higher the maximum induced emf will be. This is because more turns will result in a stronger magnetic field and a larger area for the magnetic field to change.

## 3. Can the maximum induced emf be increased by changing the magnetic field strength?

Yes, the maximum induced emf can be increased by increasing the strength of the magnetic field. This can be achieved by using stronger magnets or increasing the current through the solenoids.

## 4. What happens to the maximum induced emf if the rate of change of the magnetic field is increased?

If the rate of change of the magnetic field is increased, the maximum induced emf will also increase. This is because a faster changing magnetic field will result in a larger change in flux, which will induce a higher emf.

## 5. How does the orientation of the solenoids affect the maximum induced emf?

The orientation of the solenoids does not affect the maximum induced emf. As long as the solenoids are parallel and have the same number of turns, the maximum induced emf will remain the same regardless of their orientation.

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