Physics XXXXXXXXXX)Assignment 8Due: Thursday, March 30Hand in to drop slots on second floor of Dunn. Answer in the spaces provided. Your name (print: Last, First) Your Mark (out of 16)1....

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Physics 1551 (2023) Assignment 8 Due: Thursday, March 30 Hand in to drop slots on second floor of Dunn. Answer in the spaces provided. Your name (print: Last, First) Your Mark (out of 16) 1. Applying EM Induction to Medicine. A stent is a cylindrical tube, often made of metal mesh, that's inserted into a blood vessel to overcome a constriction. It's sometimes necessary to heat the stent after insertion to prevent cell growth that could cause constriction to recur. One method is to place the patient in a changing magnetic field, so that induced currents heat the stent. Consider a stainless-steel stent 12 mm long by 3.5 mm in diameter, with total resistance 41 m Ω . Treating the stent as a single wire loop in the optimum orientation, find the rate of change of magnetic field needed for a heating power of 210 mW [4] Hint: Remember that the power dissipated by a resistor can be given as 2. “Wireless” charging An electric toothbrush uses induction to charge its battery. We can model this as a setting up one solenoid inside another. If we choose two solenoids of the same length but different diameters and number of loops: (a) Find an expression for the magnetic field inside the inner solenoid in terms of the applied current I 1 , the number of coils N 1 , the diameter d 1 , and the length of the solenoids l . [1] (b) Find an expression for the flux experienced by the outer coil which has N 2 coils, diameter d 2 , and length l . (This coil would be located in the base of the toothbrush). [2] (c) Given that L1=6.5μ H , d 1=2.5 mm , d 2=8.0 mm , and l=4.4 mm , find the total number of coils needed for the second solenoid if the driving current I 1=(0.060 A)cos(ω t ) is expected to produce a maximum voltage of 3.6 V . Note that the frequency of the driving current is f =60 Hz . [3] In reality the number of coils is significantly smaller, as we can use an iron core to increase the inductance of the coils. 3. Eddy currents. A conducting disk with radius a, thickness h, and resistivity ρ is inside a solenoid of circular cross section. The disk axis coincides with the solenoid axis. The magnetic field in the solenoid is given by B=bt , where b is a constant and t is the time. Find expressions for: (a) The current density J (current/area) in the disk as a function of the distance r from the disk center [3] (b) The rate of power dissipation in the entire disk. [3] Hints: Use Ohm’s Law to connect the induced EMF to the current density, where V =IR , J ≡I / A , and the resistivity along a length L is defined as ρ≡RA / L . Consider the disk to be made up of infinitesimal conducting loops of width dr . The situation is similar to the aluminium plate that is dragged through the magnetic field demonstrated in class, but easier to calculate.