$[0/3$ Points$]$ SERPSE$1029\mathrm{.}4.$OP$\mathrm{.}020.$

$($a$)$ A student is experimenting with some insulated copper wire and a power supply. She winds a single layer of the wire on a tube with a diameter of $d_{\text{s}\text{o}\text{l}\text{e}\text{n}\text{o}\text{i}\text{d}}=10\mathrm{.}0cm.$ The resulting solenoid is $l=65\mathrm{.}0cm$ long, and the wire has a diameter of $d_{\text{w}\text{i}\text{r}\text{e}}=0\mathrm{.}100cm.$ Assume the insulation is very thin, and adjacent turns of the wire are in contact. What power $($in W$)$ must be delivered to the solenoid if it is to produce a field of $8\mathrm{.}00$ mT at its center? $($The resistivity of copper is $1\mathrm{.}70{10}^{-8}*m.)$

Find the number of turns by dividing the solenoid length by the diameter of the wire. Then apply the relationship between the magnetic field inside a long solenoid and the current. Use your result, along with an expression for the resistance of the wire in terms of resistivity, to calculate the power. In your calculations, you will need the length of the wire. How is the wire length related to the loop circumference and the diameter of the wire? W

What If$?$ Assume the maximum current the copper wire can safely carry is $16\mathrm{.}0$ A $.$

$($b$)$ What is the maximum magnetic field $($in T $)$ in the solenoid? $($Enter the magnitude.$)$

Apply the relationship between the magnetic field inside a long solenoid and the current. Note the current is different from the value found in part $($a$).$ T

$($c$)$ What is the maximum power $($in W$)$ delivered to the solenoid?

Use the relationship among power, current, and resistance to calculate the power delivered to the solenoid. Use the resistance found in part $($a$).$ W

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