Medical devices implanted inside the body are often powered using transcutaneous

Question

Medical devices implanted inside the body are often powered using transcutaneous energy transfer (TET), a type of wireless charging using a pair of closely spaced coils. An emf is generated around a coil inside the body by varying the current through a nearby coil outside the body, producing a changing magnetic flux. Calculate the average induced emf (in V) if each 15.0-turn coil has a radius of 1.60 cm and the current in the external coil varies from its maximum value of 14.0 A to zero in 5.75 10-6 s (Hint: Recall from Topic 19 that the magnetic field at the center of the current-carrying external coil is B-???. Assume this 2R magnetic field is constant over the interior coil's area and oriented perpendicular to the internal coil.) HINT

Explanation / Answer

Induced EMF is given by:

EMF = -N*d(phi)/dt

phi = Magnetic flux = B*A*cos theta

So, EMF = -N*A*cos theta*dB/dt

N = 15.0 turns

A = area = pi*0.016^2 = 8.04*10^-4 m^2

dt = 5.75*10^-6 sec

dB = Bf - Bi

Bi = N*u0*i/(2*R) = 4*pi*10^-7*14/(2*0.016) = 15*5.50*10^-4 T

Bf = 0 T, since icurrent = 0

So,

EMF = -15^2*8.04*10^-4*cos 0 deg*(0 - 5.50*10^-4)/(5.75*10^-6)

EMF = 17.3 V

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