- #1

- 112

- 0

## Homework Statement

An ideal solenoid is expected to generate a dipole field that falls off quickly as you move away from the solenoid. The magnetic field at distance r along the axis of the solenoid is given by B = (Mo/ 2pie) (M/r^3) In this equation the parameter M is called the dipole moment and it is equal to M = NIA where N is the number of turns, and A

the cross-sectional area of the solenoid.

Calculate the value of the M , knowing that the number of turns in the solenoid you have is 1080 and the corss-sectional diameter is about 7.5 mm. Enter your measurements from the table above into the Logger Pro program and plot B vs r for each side of the solenoid. Then, perform a “variable power” fit of the form Y=AX^n with n set to -3 and identify the value of of the fit parameter A

Using the data you now have determine the value of the permeability of free space Mo

## Homework Equations

B= Mo I N / L

B = (Mo/ 2pie) (M/r^3)

## The Attempt at a Solution

The magnetic field at distance r along the axis of the solenoid can be determined. Breaking down the equation; N= number of turns, A= cross-sectional of solenoid area, M= dipole moment (M=NIA).

A= 7.5mm (diameter) = 0.0075m= 0.00375m (radius) =pr^2 = 4.4x10^-5m^2

Calculating the value of M; M= (1080 turns)( 4.4x10^-5m)(0.03A)

M= 1.43x10^-3 (dipole moment)

Using the data from the chart, a graph was established by inputting both sets of measurements from each side of the solenoid. A variable power fit in the form Y=Ax^n was done with n being set to -3, resulting in A = 5.56 x 10^-12 +/- 1.26x10^-11

Does my graph look right? I don't know where to go from here, I've repeated this lab 3 times now and am completely stuck...Im told that ' What you want to do is to compare your fit (Y = Ax^n, with n=-3) to the theoretical relation (B = (u0/2pi)(M/r^3) ) . Comparing the two formulae can tell you what the fitted parameter "A" represents.' I am not sure how to go upon that...please help me in any way