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A solenoid of length 0.700 m having a circular cross-section of radius 5.00
cm stores 6.00 μJ of energy when a 0.400-A current runs through it. What
is the winding density of the solenoid? (μ0 = 4π × 10-7 T • m/A)

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For a technical application, an electrical engineer needs to create a solenoid using copper wire with diameter d = 0.500 mm. The resistance of the solenoid needs to be 5.10 2 and the magnetic field of the solenoid with a current of 3.10 A should be 5.90 x 10-2 T. Assume the resistance does not change significantly with temperature, and the radius of the solenoid is 1.00 cm. (Use p = 1.70 x 1080 m for the resistivity of copper.) (a) How many turns of wire does the electrical engineer need? turns (b) Determine the required length (in cm) of the solenoid. cm
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