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Problem 8 Easy Difficulty

Transcranial magnetic stimulation (TMS) is a noninvasive technique used to stimulate regions of the human brain. A small coil is placed on the scalp, and a brief burst of current in the coil produces a rapidly changing magnetic field inside the brain. The induced emf can be sufficient to stimulate neuronal activity. One such device generates a magnetic field within the brain that rises from zero to 1.5 T in 120 ms. Determine the induced emf within a circle of tissue of radius 1.6 mm and that is perpendicular to the direction of the field.

Answer

1.005 * 10^{-4} V

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Video Transcript

we're told that a small coil is placed on the scalp and a brief burst of current in the coil produces a rapid changing magnetic field. So this is an induced in meth that could be sufficient to stimulate this neural activity, and the brain tissue is going to rise from a magnetic field of zero. So the initial a zero to be final, which is 1.5 Tesla and a time of 120 milliseconds, or 1200.12 seconds. And we're told that the circle of tissue is a radius of 1.6 millimeters, or 1.6 times minus three meters perpendicular to the direction of magnetic field so they do here is going to be equal to zero. So the induced E M f here is equal to the magnitude of the change in the magnetic flux, divided by the change in time Delta T Well, the changing magnetic flux is the change in the magnetic field Delta bi times the area which is pi r squared times the coastline of the angle, which is data still divided by Delta T. Well, Delta Bi is be final minus the initial, So that's gonna be 1.5 and we know all the other values and this and this expression, So plugging those in, we find that this is equal to one times 10 to the minus for the units here, Volts, Mickum box said in his air solution to the question.

University of Kansas
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University of Michigan - Ann Arbor

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McMaster University

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