Maximize the magnetic field in a solenoid

[anonymousphys]

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?

 

[Stonebridge]

The equation listed looks like the one for a (flat) circular coil.
The one used is for a long solenoid.
The field in the centre of such a solenoid is given by
B= μonI
where n is the number of turns of wire per unit length.
Your reasoning is correct if the question refers to a solenoid.