Stimulating the brain In transcranial magnetic stimulation...

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.

Key Concepts

Rate of Change of Magnetic Field

The rate of change of the magnetic field is a key factor in determining the magnitude of the induced emf. According to Faraday's Law, a more rapid change in the magnetic field results in a larger induced emf. This concept is vital in applications where precise control over the induced electrical currents is necessary, such as in various stimulation techniques or modern electromagnetic devices.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a time-varying magnetic field through a closed loop induces an electromotive force (emf) in the loop. This fundamental principle underpins the working mechanism of devices that convert magnetic energy into electrical energy, and it is essential for understanding how changes in magnetic fields generate currents in conductive materials.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing perpendicularly through a given area. It is calculated as the product of the magnetic field strength and the area through which the field lines pass. Understanding magnetic flux is crucial because it forms the basis for quantifying how much of the magnetic field interacts with a conductor, which in turn determines the induced emf according to Faraday's Law.

Induced Electromotive Force (emf)

Induced emf is the electrical potential generated in a loop or conductor due to a change in magnetic flux according to Faraday's Law. This concept is central to the design and function of many electrical and electronic systems, as it describes how mechanical or magnetic changes can be harnessed to generate electrical energy, with practical applications ranging from power generation to medical therapies.

Transcript

00:01 This question deals with transcranial magnetic stimulation.

00:04 The tms treatment is very simple.

00:07 What you do is you put a small coil of wire that is connected to an external power source above near the patient's scalp, and you can change the current through this coil, which then will lead to a change in the magnetic field that is produced by this coil.

00:24 This magnetic field is able to penetrate the patient's head, and it will affect a small region in the brain.

00:33 And as the magnetic field changes, the magnetic flux through this small region in the brain will change as well.

00:42 Now we know from magnetic induction that as the magnetic flux changes, you will have an induced current going through the small region of brain.

00:51 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.

01:03 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.

01:13 Therefore, there's going to be an abrupt decrease in the magnetic field, thereby decreasing the magnetic flux going through the small region in the brain, and that also means we're going to induce a current.

01:28 But let's first write out our givens here.

01:32 So we know that initially the magnetic field is about 0 .80 tesla.

01:38 Afterwards, it is reduced down to 0 in a short amount of time that is 0 .08 seconds.

01:47 And they're asking us to find the small induced emf.

01:54 So that's our goal.

01:57 And they also tell us that the radius of this region in the brain is 1 .2 times 10 to the negative 3rd meters...

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