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## Homework Statement

It is desired to construct a solenoid that has a

resistance of 9.94 Ω (at 20◦C) and produces a

magnetic ﬁeld at its center of 0.0224 T when

it carries a current of 5.17 A. The solenoid is

to be constructed from copper wire having a

diameter of 0.517 mm.

Find the number of turns of wire needed if

the radius of the solenoid is to be 2.2 cm. The

resistivity of the copper is 1.7 × 10−8Ω · m .

Answer in units of turns.

## Homework Equations

magnetic field = B = (vacuum permeability/2)*((number of turns*current)/(resistance))

Resistance = resistivity*(length/area)

## The Attempt at a Solution

To start off I solved for the number of turns using the first relevant equation.

number of turns = ((2*resistance*B)/(vacuum permeability*current))

At this point I thought: Well the wanted resistance must be the resistance and so I went on plugging the numbers in and it was wrong...

Then I noticed that I need to specify how large the radius is and I don't see a radius variable inside of one of the equations. I'm basically stumped, and I feel like I'm missing an equation or something...Also any ideas as to why they are giving so much information?