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Problem 21

To measure a magnetic field produced by an electr…

06:39
Problem 20

Stimulating the brain In transcranial magnetic stimulation (TMS) an abrupt decrease in the electric current in a small coil placed on the scalp produces an abrupt decrease in the magnetic field inside the brain. Suppose the magnitude of the $\vec{B}$ field changes from 0.80 $\mathrm{T}$ to 0 T in 0.080 s. Determine the induced emf around a small circle of brain tissue of radius $1.2 \times 10^{-3} \mathrm{m}$ . The $\vec{B}$ field is perpendicular to the surface area of the circle of brain tissue.

Answer

a) $\frac{1}{2}$
b) $\frac{1}{2}$


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Video Transcript

this question deals with transcranial magnetic stimulation. The TMS treatment is very simple. What you do is you put a small coil wire that is connected to an external power source above um, near the patient scalp, and you can change a current through this coil, which then will lead to a change in the magnetic field that is produced by this coil. This magnetic field is able to penetrate the patient's head, and it will affect a small region in the brain and asked the magnetic field changes. The magnetic flux through this small region in the brain will change as well. Now we know from magnetic induction that asked the magnetic flux changes. You will have an induced current going through the small region of brain. So doctors and researchers have used this treatment to help treat mood disorders, Parkinson's disease, Huntington's disease or other diseases that deal with the nervous system. So in today's question, we are given a scenario where there is going to be an abrupt decrease in the electric current in the small coil. Therefore, there's going to be up an abrupt decrease in the magnetic field, thereby decreasing the magnetic flux going through the small region of the brain. And that also means we're going to induce a current. But let's first right out our givens here. So we know that initially the magnetic field is about 0.80 Tesla's afterwards is reduced down to zero in a short amount of time. That is your 0.8 seconds, and they're asking us to find the small induced E M f. So that's our goal. And they also tell us that the radius of this region in the brain is 1.2 times 10 to the negative third meters. They also tell us that the magnetic field is perpendicular to the surface area on the brain tissue, so the angle in question is 90 degrees. To solve this question, we need to remember, um, the relationship between E. M. F and all of these given variables. Now, today we're just going to find the magnitude, so I'm not going to worry about the sign of my answer. So Yemma is equal to the number of turns in the coil times. Thea absolute value of the change in magnetic clucks over the changing time. So because the number of turns that we have here is one we can just safely ignore the end right here. As we work out this question, we also remember that flux is calculated us be my knight. Feel times the area that it is penetrating times co sine of the angle between these two vectors. Well, we do have enough information to saw four area, and we know the angles 90 co sign of 90 is one. So this turns out to be an unnecessary part of our calculation as well. The only thing to note is that the changing flux actually comes from the change in the magnetic field. Because that's the only thing. According to our givens, that has a change. So let's put all of those things together. So, um, f is equal to and we're just one, so we don't care. Sometimes the absolute about is equal to the absolute value of the changing. Be so final minus initial finalists zero minus initial, which is cereal 00.8 zero. Um, times. Theo area well area of a circle is just going to be high r squared, right? So it's going to be pi times. Oh, are, which is 1.2 times 10 to the native third meters squared times co sign of 90 which is one. So we don't have to write it here all over the changing time and the time interval is 0.8 seconds. So after a punching all that into the calculator, the final result turns out to be 4.52 times 10 to the negative fifth Fultz.

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