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.
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?