PART C,D,ELAST 3 PARTS ONLY PLEASE 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?

c As given, Change in temperature ∆T due to transfer of electrical energy into thermal energy is…

lies Suppose a magnetic field B(t) oscillates with frequency w. A circular loop of copper perpendicular 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 the induced emf & in the loop of wire and use this to calculate the current generated in the loop as a function of time. b. What is the power dissipation in the wire as a function to time? Make a sketch of this function. What is the average power Pave dissipation in the wire? Hint: what is the average value of the function you sketched? C. Recall that power is a rate of energy transfer, and that power dissipated by a resistor leads to a change in the thermal energy of the material (in this case the copper wire). We can relate a ΔΕth change in thermal energy to a change in temperature by AT where M is the total mass and c = Mc is the specific heat capacity of the material (see page 526 for details). Find an expression for a dT differential change in temperature of the copper wire loop. dt d. Suppose the copper is initially at some temperature To. Find an expression for the temperature 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 loop is 2.0 cm. Assuming the initial temperature was To = 283 K, calculate the temperature of the copper loop after 1.0 minute of exposure to the oscillating magnetic field. The mass density of copper is Pm = 8.96 g/cm³. The resistivity of copper is found in table 27.2 and the specific heat capacity is found on page 526. Express your answer in °C. Comment on the result. Is this a large change in temperature? Suggest a practical application for this technology. How could this be used?