Please help designing a specific electromagnet

[checkmatescott]

[/ATTACH][/ATTACH]I need some help designing my electromagnet because I am a bit lost with it
I need to work out the gauge of the wire to be used,
the resistance of the wire needs to match the battery's internal resistance for max power transfer
I need to work out the most amount of turns i can have
I need to work out how much inductance this coil has to then work out the time constant for that coil
this time constant MUST be below 0.0008 seconds and above 0.0007s for the purposes of my build
I have a few equations that i think may help and i think I am almost there but i just can't work it out

heres what i have if more info is needed for anything just tell me and i will find it thanks again for any help its really appreciated thanks a lot in advance

B * gap = Mu * N * I

B is in Tesla (10,000 gauss)
gap is in meters (This is the opening of the "C ".)
Mu = 4π * 10-7
N is an integer equal to the number of turns in your coil
I is the current in Amps

Another famous law, called Ohms law, tells you the relationship between amps, volts and resistance.

Volts = Amps * resistance (measured in Ohms)

Your coil should be made so it has a voltage drop equal to what your battery can put out at the best rate of discharge. A piece of copper has resistance which can be determined form the following formula.

Resistance = Rho * L / A

Resistance is in Ohms
Rho is a constant for each metal and for copper it is 1.6*10-6 ohm-centimeters
L is the length of the wire used in centimeters
A is the cross section area of the copper wire in centimeters squared

here is an inductance calculator for sqaure loop http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_calculator


I also have this picture but it isn't very clear to me and i have drawn a diagram to show the dimentions of the core

 

[checkmatescott]

also I've worked out abit more i need 500 turns with a resistance of 290 ohms how do i work out the gauge and length of the wire?

 

[SirAskalot]

You have two equations and two unknowns; L , A. Should be basic algebra.

R = rho * L / A
L = 500 * "circumference of one turn" <---- given by geometry of your coil/core

 

[checkmatescott]

THANKS FOR THE QUICK RELPY my core is 8 centimeters in circumfrence and it is square does it matter i also have another equation L= N^2*uAl / l
L = inductance
N = number of turns
u = absolute permeability of core material
A cross sectional area in meters
l = average length of coil in meters

how do i work out the gauge of the wire