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It is desired to construct a solenoid that will have a resistance of 4.60 Ω (at 20.0°C) and produce a magnetic field of 3.50 10-2 T at its center when it carries a current of 3.50 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm.

(a) If the radius of the solenoid is to be 1.00 cm, determine the number of turns of wire needed.

(b) If the radius of the solenoid is to be 1.00 cm, determine the required length of the solenoid.

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