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# Electrical Engineering/Calculating the field strength of an electromagnet formed of a less conductive material

Question
QUESTION: Hi Cleggsan,

I hope this message find you well. A while ago you gave me some great help with calculating the strength of a solenoid. I have design for a solenoid where the coil is formed with a conductive silver paste. This paste less conductive than say, copper wire and I am wondering how this lower conductivity would affect the magnetic field strength.
None of the formulas I have found for calculating a solenoid's magnetic field mention anything about the conductivity of the solenoid's coil material. If the conductivity of the the coil material is lower, does this mean the solenoid's magnetic field strength will also be lower?

Thanks and best regards,
Eddie

ANSWER: Well the resistance and voltage applied is the key issue. In order to retain the proper current level in the coil you must have the same current. If the resistance of the silver paste is too low you would need to increase the voltage in order to get the current needed.  Ohm's law is at work as always: Voltage equals Current times Resistance or E=I*R.

Actually, silver is a highly conductive material, lower resistance than copper for example, but in paste form it may be diluted to point of very low resistance.

Keep working; always good to hear from you.  Hope you can become successful with your experimentations and product development ideas.

Domo. Domo.

---------- FOLLOW-UP ----------

QUESTION: Thanks for the encouragement Cleggsan!

I am pretty sure I understand but, I am wondering if you could tell me whether some assumptions I have made are reasonable.
If I want to estimate the limits of the maximum safe level of current I can put through the conductive paste deposits, can I use the diameter of the paste deposit, and the percentage of metal filler as a guide? For example a deposit that is 1mm diameter with a silver particle content of 70% being equivalent to a 0.7mm diameter copper wire? (After the higher conductivity of the silver has be taken into account)

Itsumo arigato gozaimasu!

Yes, basically.  But, the percent of metal filler does not relate to resistance; it is probably a non-linear ratio and dependent to some extent on the filler's resistivity as well.  I suspect some testing might be necessary in order to know how much resistance you'll get and if a temperature rise during conduction will alter the current levels.

As to the 70% being equivalent to .7mm wire it may be an approximation but I still recommend some sort of testing to know for sure.

Achtung.

Electrical Engineering

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#### cleggsan

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