Strongest possible electromagnet for school.?

Question

What design would make the most efficient electromagnet. Must lift most paperclips. Then the number of paperclips will be divided by the current to get the efficiency. It cannot exceed 125 cm cubed in volume. It will be hooked up to a 5 volt power source. The wire hook in leads need to be at least 30 cm long. I cant use wire more than 1 mm in diameter. The resistance can't be under 0.5 ohms.

Answer 1

The more ampere-turns you will get the stronger will the magnet be. This is an optimization problem. 1mm diameter wire is much too heavy. Start with a 24 gage wire.

Below are the theory and wire data.

F=(B)^2 A/u
F- force
B- magnetic field (about 1 Tesla is about max, to be ion the safe side, before you saturate your core)
A - area of the core (use iron rod or A1)
u - permeability of free space

B= u N I/L
N - number of turns
I - current
L - length of the coil

I max = Vcc/Rmin= 5/.5=10A (this is maximum value)

Start your calculations with B=1Tesla
Iron core .75 inches in diameter A= 11.4cm^2 that would give you about 5cm in length. the amount of copper you can pack is about 90 to 80% of an area A2. A2=L(Dt-D1)/2
Dt=sqrt((125-5 A1)/pi)=sqrt((125- 5(11.4))/pi)=4.6 cm
A2=5 (4.6-1.905)/2= [note 3/4"=1.905 cm]
A2=6.75 cm^2 (= 1.04 inches square)

Number of turns N= A2/(area per wire crossection)
for 30 gage N=1.04 /(3.14159.. (10/1000)^2)=3300 turns
average length of the wire Lw= pi (average D) (N)
Lw=pi ((Dt+D1)/2) N=
Lw=3.14159 ((4.6 cm+1.905 )/2) 3300=33720 inches (2810ft)
R=290 ohms
The key is you have to get max NI and max core area.

Note 1: Be careful not to mix British units (lb/feet/sec) and standard(kg/meter/sec)
Note2 : when computing resistance 1 mil=1/1000 of an inch.

Answer 2

If it were me I'd use #30 AWG wire, with about 200 - 350 turns on the core. I'd make sure my core was at least 3-4 inches in length so I can get the most turns per layer. I'd use wire that is insulated with enamel only ( also known as speaker or coil wire) because the insulation is thinner.
I would also place a washer on both ends of my core, also when wrapping your core " TRY" very hard no to cross turns or leave space between them, this will reduce the field created.