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.
Answered 1 days AfterMar 29, 2023

Answer To: Physics XXXXXXXXXX)Assignment 8Due: Thursday, March 30Hand in to drop slots on second floor of...

Dr Shweta answered on Mar 31 2023
33 Votes
Ans 1. The power required is 210 mW, then the current is calculated as:
P = I2R
210 X 10-3 = I2(41
X 10-3)
I = 2.26A
And the induced EMF is calculated as = ΔBA/Δt
Under optimum orientation, area is equal to the circle of stent
Area = πr2 = π (1.75 X 10-3)2 = 0.96 X 10-5 m2
EMF is calculated using IR as
Now, to the rate of change of the magnetic field ΔB/Δt is calculated as
ΔB/Δt = IR/A = (2.26) (41 X 10-3)/0.96 X 10-5
ΔB/Δt = 9.65 X 103 T/s
Now, E = dΦ/dt = d(BA)/dt = AdB/dt
also, P = E^2/R
so, P = (AdB/dt)2 /R
so, dB/dt = √(PR/A2)
= √(210*10-3*41*10-3/(π*(1.75)2)2)
= 0.0966 Tesla /sec
Ans 2 (a) The magnetic field inside the solenoid is calculated as:
B = μ₀ N I / L
here μ₀ = permeability of free space,...

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