Q: If 55.8 cm of copper wire (diameter = 1.00 mm) is formed intoa circular loop

Question

Q: If 55.8 cm of copper wire (diameter = 1.00 mm) is formed intoa circular loop and placed perpendicular to a uniform magneticfield that is increasing at a constant rate of 77.3 mT/s, at whatrate is thermal energy generated in the loop? Give the answer inmicro-Watt (W) and to two decimalplaces. (micro = = 10-6) Q: If 55.8 cm of copper wire (diameter = 1.00 mm) is formed intoa circular loop and placed perpendicular to a uniform magneticfield that is increasing at a constant rate of 77.3 mT/s, at whatrate is thermal energy generated in the loop? Give the answer inmicro-Watt (W) and to two decimalplaces. (micro = = 10-6)

Explanation / Answer

R is the resistance in the wire is the resistivity of the copper =1.69x10-8m L is the length of the wire = 0.558m A is the cross-sectional area of the wire =0.500x10-3m The resistance is given by     R = L/A, The resistance is given by     R = L/A,         =((1.69x10-8m)(0.558m))/((0.500x10-3m)2)        =1.184x10-2.
If B is the magnitude of the magnetic field through theloop, then according to Faraday's law                            = (AdB)/(dt) where A is the area of the loop. The radius of the loop is r = L/2        Area isr2 =(L2)/(42)                          = L2/4 Then = (L2/4)(dB/dt)              =((0.558m)2/4)(77.3x10-3T/s)             =1.9162x10-4V. The rate of the rmal energy generation is          P =2/R            = 3.101 * 10-6W          

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