Formula for the strength of an electromagnet

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SUMMARY

The strength of an electromagnet can be calculated using the formula B = μ N I / L, where μ is the permeability of the core material, N is the total number of turns, I is the current in amperes, and L is the length of the iron core in meters. The permeability μ is defined as μ = μ0 * μr, with μ0 being a fundamental constant and μr the relative permeability of the core material. For accurate calculations, it is essential to use consistent units, preferably meters for length, and to consider the total number of turns without accounting for multiple layers. A solenoid with a length of 0.1 meters, 200 turns, and an iron core with a relative permeability of 200 yields a magnetic field strength of 0.5 Tesla at 1 ampere.

PREREQUISITES
  • Understanding of electromagnetism principles
  • Familiarity with magnetic permeability (μ0 and μr)
  • Knowledge of solenoid construction and parameters
  • Basic proficiency in unit conversions (meters to inches)
NEXT STEPS
  • Research the calculation of magnetic fields in solenoids using the formula B = μ N I / L
  • Explore the properties of different core materials and their relative permeabilities (μr)
  • Learn about the impact of current variations on electromagnet strength
  • Investigate the effects of coil layering on magnetic field strength
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Mindstormed
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Trying to determine the strength of an electromagnet in Teslas, with an iron core.
Some sites have the same basic formula but with different units after B=

Some use μ0, μr, or μ. Which one to use?

For N (the number of turns), is this the general number of turns accounting for multiple layers, or turns per meter (or inches), or what?

And L (the length), is it the length of the iron core or the length of the wire used, and should it be in meters or inches?

According to this site (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html), a 0.1 meter (4") length solenoid (I'm assuming their talking about the iron core?) with 200 turns, 1 amp, and an iron core with 200 relative permeability is 0.5 Tesla. With 3 amps, this is about 1.5 Tesla and that doesn't sound right.

Any help is appreciated, thanks!
 
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Mindstormed said:
Some use μ0, μr, or μ. Which one to use?
μ = μ0 * μr
μ0 is a fundamental constant, you also need μr for your core material, or the book may just list μ and do the multiplication for you.

For N (the number of turns), is this the general number of turns accounting for multiple layers, or turns per meter (or inches), or what?
Just the total number of turns.

And L (the length), is it the length of the iron core or the length of the wire used, and should it be in meters or inches?
It's the length of the core that has coils wrapped around it.

You can use any units you like, as long as you have matching units for μ.
It's probably safest to use metres for everything.

a 0.1 meter (4") length solenoid (I'm assuming their talking about the iron core?) with 200 turns, 1 amp, and an iron core with 200 relative permeability is 0.5 Tesla. With 3 amps, this is about 1.5 Tesla and that doesn't sound right.
Nope that sounds a bit high.


μr iron = 5000 μr steel = 200 (varies a lot!)
B = μ N I / h = 200 * 4pi*10^-7 * 200 * 1 / 0.1 = 0.5T
which still sound s a lot - but this is the field inside the core - the field outside the coil is much lower.
 
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