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## Homework Statement

We want to construct a solenoid with a resistance of 4.30 Ω and generate a magnetic field of

3.70 × 10−2 T

at its center when applying 4.60 A of electrical current. We want to use copper wire with a diameter of 0.500 mm. If we need the solenoid's radius to be 1.00 cm, how many turns of wire will be need?

## Homework Equations

B = μ IN /L

## The Attempt at a Solution

I was thinking the height of the solenoid would be the diameter, which is the height of a wire, multiplied by the number of coils. I know that the solenoid is proportional to the number of coils. How can I judge the number of coils of a solenoid given

(1) the resistance...

The greater the number of coils is the greater resistance? By finding the resistance of one loop of copper with certain radius and diameter?

(2) magnetic field

The only equation I know with magnetic field of a solenoid is one derived using Ampere's law. so B = μ IN /L. Certainly I can find the magnetic field of one loop where L is equal to the diameter of wire. This seems like a solid approach.

(3) radius

Why does radius matter? If the radius increases, the length must increase sevenfold. My equation leaves out radius so I believe radius does not matter.