Resolved: "Does an electromagnet increase in strength more by..."

sublimnes9

Answered question

2022-08-09

Does an electromagnet increase in strength more by voltage or wire turns?

Kelton Glover

Beginner2022-08-10Added 17 answers

The magnetic field in a solenoid of length

L

around an iron core with

N

turns is given by:

B = μ \frac{N I}{L} .

Assuming some Ohm's law type of resistance in the wire we can replace

I

with

V / R

to get

B = μ \frac{N V}{L R} .

So the magnetic field strength increases linearly with both the number of turns and the voltage. The resistance of a wire is given by

R = ρ \frac{l}{A},

(where

ρ

is some material property of the wire,

A

is the cross sectional area and

l

is the length) so that

L R = ρ L l / A

and

B = μ \frac{N V A}{ρ L l} .

r

is the radius of the wire (

π r^{2} = A

) then

2 r N \approx L .

. (Think of stacking the rings of wire on top of each other.) These last substitutions yield

B = \frac{μ π r}{2 ρ} \frac{V}{l} .

This seems to suggest that increasing the voltage has the same effect as shrinking the length of wire used.

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