## Is cross-sectional area of a coil related to it magnetic field strength

I have to desgin an experiment for physics and and my research question is going to be:
How does the cross-sectional area of the solenoid’s coil affect the strength of its magnetic field?
This is my hypothesis, my question is if you think the reasoning is valid.
I believe I should find it is proportional to some power of the area and that it should follow a positive correlation as the magnetic field strength is directly proportional to the velocity (current) and the number of moving charges contributing to the magnetic field, which assuming a conductor with constant width and resistivity, would mean it is proportional to the length. Therefore, if the length of the coil is the same, the length of the wire will be proportional to some power of the cross-sectional area of the coil. As the length of the coil is approximately L=N(2πr), where N is the number of turns and r is the radius of the circumference of each turn, and the area is A=πr^2, we can represent length in terms of area:
L=N(2√π)(√A)
Hence:
L∝A^(1/2)
Therefore, as we said that magnetic field strength, B, is directly proportional to the firs power of L, we can also say that:
B∝A^(1/2)

Thank you,

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 you can use area and the magnetic field strength to find the magnetic flux, which describes the amount of electric field lines over a cross sectional area. from wikipedia: "Magnetic flux (most often denoted as Φm), is a measure of the amount of magnetic B field (also called "magnetic flux density") passing through a given surface (such as a conducting coil). The SI unit of magnetic flux is the weber (Wb) (in derived units: volt-seconds). The CGS unit is the maxwell." Also, you can use the rate of magnetic flux to find the voltage of an emf source, such as your coil, and use the amount of turns the wire makes around the coil to find the voltage the emf exerts. Emf=(N) times (change in Magnetic flux/change in time) where change in magnetic flux= (final area times magnetic field times cos theta)-(initial area times magnetic field times cos theta) Then you can find the current by diving by the resistance of the system, but idk if you can do that. there might be another way of finding current using voltage that idk.