Magnetic field strength dependent on distance from source

mrv11

I have a practical question to add...

Using a calculator found here: http://hyperphysics.phy-astr.gsu.edu...lenoid.html#c3

I can calculate the magnetic field within a given solenoid. To verify this I have a measured current flowing through the wire and a compass. I align the solenoid at a right angle to the earth's magnetic field and bring the solenoid closer to the compass until it is deflected 45 degrees.

Therefore using vector analysis, I know the field produced by my solenoid at this distance to be equal to the field of the earth at my location (roughly 4.0 x 10^-5 Tesla).

To verify the calculated magnetic field strength in my solenoid do I use the a re-arranged version of
B=(μ₀NIA)/(2∏x³) ?
N= number of turns

I cannot imagine B_solenoid=B_{at compass}r³ would work... The dimensional analysis would leave me with improper units!

Thank you in advance!

jtbell

See here for the magnetic field along the axis of a finite solenoid:

http://www.phys.uri.edu/~gerhard/PHY204/tsl215.pdf

This assumes the solenoid has no iron or other magnetic material inside it.