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## Homework Statement

Assuming we have equal volumes in both scenarios, which would maximize the magnetic field in a solenoid: a thick and short wire or a thin and long wire.

## Homework Equations

B=(m)(constant)(I)/(2R)

m= the number of layers of wire

## The Attempt at a Solution

The answer is clearly a thin and long wire because of the equation B=unI, but I was suppose to use the equation I listed under "relevant equations". According to that equation, if we use a thicker wire, the number of layers of wire would increase but the radius would increase. So based on that equation, how am I suppose to realize that a long and thin wire maximizes the field?