Suppose a magnetic field B(t) oscillates with frequency w. A circular loop of copper liesperpendicular to the magnetic field. The radius of the circular loop is r.a.Write down an expression for the magnetic field as a function of time. Determine theinduced emf & in the loop of wire and use this to calculate the current generated in the loop as afunction of time.b.What is the power dissipation in the wire as a function to time? Make a sketch of thisfunction. What is the average power Pave dissipation in the wire? Hint: what is the average value ofthe function you sketched?C.Recall that power is a rate of energy transfer, and that power dissipated by a resistorleads to a change in the thermal energy of the material (in this case the copper wire). We can relate achange in thermal energy to a change in temperature by ATwhere M is the total mass and cΔΕthMcis the specific heat capacity of the material (see page 526 for details). Find an expression for adT-differential change in temperatureof the copper wire loop.dtd.Suppose the copper is initially at some temperature To. Find an expression for thetemperature of the loop as a function of the time T(t) it is exposed to the oscillating magnetic field.Hint: Integrate.e.Suppose that a 10.0 mT magnetic field oscillates at 1000 Hz, and the radius of the loopis 2.0 cm.Assuming the initial temperature was To = 283 K, calculate the temperature of the copperloop after 1.0 minute of exposure to the oscillating magnetic field. The mass density of copper isPm = 8.96 g/cm³. The resistivity of copper is found in table 27.2 and the specific heat capacity isfound on page 526. Express your answer in °C. Comment on the result. Is this a large change intemperature? Suggest a practical application for this technology. How could this be used?

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