# Magnetic flux / induced emf problem

## Homework Statement

A single coil with a radius of .02m is placed inside a 3m long solenoid that has 600 turns. The radius of the solenoid is 0.15m. The plane of the coil is perpendicular to the axis of the solenoid. The solenoid is connected to a battery, an ammeter and a switch. The ammeter reachs 5A in 0.2 seconds and remains constant.

a) What is the change in the magnetic flux across the small loop?
b) What is the average induced emf in the small loop?
c) Another solenoid has an inductance of 8.0 henries and a resistance of 2.772 Ohms. It is connected to a battery and a switch. How long does it take for the current to reach half of its maximum value after the switch is closed?

Ahhh... crap. This problem is hard for me.

## Homework Equations

I know the equation for magnetic flux is:
Phi = (B*A*cosPhi)
B is the magnetic field, A is area.

## The Attempt at a Solution

I don't know how the coil relates with the solenoid. Should I first figure out what is going on inside the solenoid? Then from there I could figure out the emf of the single coil? I'm lost. I'm having trouble conceptualizing this problem. Any help is greatly appreciated. Thanks!

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Doc Al
Mentor
I don't know how the coil relates with the solenoid. Should I first figure out what is going on inside the solenoid?
Absolutely! What's the field inside the solenoid? That's the field that is creating the flux through the coil.

Great.

The formula to find the field inside of a solenoid is B = Mu*Number of turns*Length of solenoid*I. Using this, I found the field to be 0.0113T.
Magnetic flux = BAcosPhi
When plugging in my B value from the field inside the solenoid and the area (Pi*r^2) of the coil and cos 0, my value is off. I get 1.42E-5. What I'm looking for is 1.58E-6.

Can you help me? Where did I go wrong?

Doc Al
Mentor
The formula to find the field inside of a solenoid is B = Mu*Number of turns*Length of solenoid*I.
The correct formula is μ*(N/L)*I.

Ahh yes...

using Mu*(N/L)*I, I returned a value of .0013 which fit nicely into my change in magnetic flux equation to give me the correct answer.

Thanks a lot!