Physics XXXXXXXXXX)
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 afte
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 cu
ents heat the
stent.
Consider a stainless-steel stent 12 mm long by 3.5 mm in diameter, with total
esistance 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 tooth
ush 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 cu
ent 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
ase of the tooth
ush). [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 cu
ent 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 cu
ent 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 cu
ents.
A conducting disk with radius a, thickness h, and
esistivity 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 cu
ent density J (cu
ent/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 cu
ent density, where V =IR , J ≡I / A , and the
esistivity 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.