# Electromagnetic and Magnetic Levitation Answered

Hi! I am setting up a levitation system and need to estimate the amount of voltage and current that is needed for a 2" dia. coil to produce 4800 Gauss. I don't have any restrictions/requirements on the core, number of turns, etc as long as it would produce 4800 Gauss with a 2" diameter. How can this be calculated? (I have spent a lot of time googling for such information, but I am pretty confused and didn't find how to calculate this) Thanks!

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This is one of the most obscure parts of conventional (ie non-quantum, etc) physics. I had to go and look it up, and on finding it I realised why.

See the equation below, which I lifted from this paper.

To find the field strength in Tesla ( = 10,000 Gauss), multiply the number of turns in the coil, radius of the coil in metres, the current flowing and the permeability of vacuum (4pi * 10-7) together, then divide by ((the radius2 + the axial distance from the coil2) 1.5), then halve the result.

To find the number of turns and current, you will need to set B=0.48T (=4,800 Gauss), a=0.05 (2" = 5cm = 0.05m) and z=the required distance in metres and solve the equation. This could get a bit weird as you have a fractional power on the bottom of a fraction- get a large piece of paper and put your algebra hat on.

Alternatively, if you feel like doing groundwork to make your life easier later on, write a calculator in a spreadsheet that lets you plug numbers in and calculates the field, then play with the numbers until you reach something achievable.

This is the equation.

u0 is the permeability of vacuum, 4pi*10-7 or about 0.0000012566
N = turns
I = current (Amps)