# Calculating magnetic field for a micro solenoid

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1. Mar 6, 2015

### EddieP

I am trying to calculate the magnetic field (in tesla/gauss) of an iron core electromagnet that is very small and has very few windings. For example 12 windings over 0.003 meters. I know this is not going to produce a very strong field, but I would like to pulse a strong current through the coil very briefly to make it stronger. I have found an number of sources listing the formula for the calculation of magnetic field strength -

B = permeability * turn density * current = (μ * μ0)*(number of turns/core length)*current

listed here http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

My question is - can this formula be applied to my electromagnet design? Does the size and low number of windings on my electromagnet mean this formula is not valid? Is there any other way I can calculate/estimate magnetic field?

2. Mar 6, 2015

### tech99

The magnetic path is partly made of air, which has a relative permeability of 1. This means that the reluctance of the total path will be more than for the iron alone. Therefore for your fixed value of magnetising force, the flux will be reduced by perhaps half. The flux density is B and is dependent on the cross sectional area of the path at a given point, and will reduce as the field spreads out into the air, depending on the distance. So basically, you need more ampere turns than the simple formula.