You wish to construct a solenoid with a diameter of 2.00 cm that will produce a magnetic field of $7.80 \times 10^{-2}$ T at its center when a current of 18.0 A is passing through the coils. You want the resistance of the coil wire to be 3.40 $\Omega$. The resistivity of the wire used is $1.70 \times 10^{-8}\ \Omega \cdot m$ (at 20.0°C), and you are using a wire that has a cross-sectional area of $3.14 \times 10^{-8}\ m^2$. (Note that this solenoid may not necessarily be so tightly wound that the adjacent loops of wire will touch each other. Nonetheless, you may assume that it behaves like an ideal solenoid.) Determine the following:(a) Number of turns needed on the solenoid \[ \_\_\_\_\_\_ \text{ turns} \](b) Length of the solenoid \[ \_\_\_\_\_\_ \text{ m} \]

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