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Problem 12 Easy Difficulty

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 if each 10-turn coil has a radius of 1.50 cm and the current in the external coil varies from its maximum value of 10.0 $\mathrm{A}$ to zero in $6.25 \times 10^{-6} \mathrm{s}$ . (Hint: Recall from Topic 19 that the magnetic field at the center of the current-carrying external coil is $B=N \frac{\mu_{0} I}{2 R}$ . Assume this magnetic field is constant and oriented perpendicular to the internal coil.)

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Video Transcript

So to find the induced e m f, we had to first find the magnetic field using the equation they gave us A B is equal to mu, not a magnetic permeability of free space times the number of turns times the current divided by two times the radius. So I found that to be 4.19 times 10 to the minus three test love. So now we can go ahead and calculate the induced you met, which is equal to the change in flux. Delta Phi divided by the change in time Delta T Okay, well, Delta Phi is equal to the number of turns times the magnetic field times the area which is pi r squared, divided by still the change in time Delta T which we were told a 6.25 times 10 minus six seconds. Playing all those values into this expression, we find that this is equal to four 0.74 in the units Here are volts weaken box that it is the solution to our question

University of Kansas
Top Physics 102 Electricity and Magnetism Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Physics 102 Electricity and Magnetism Bootcamp

Lectures

Join Bootcamp