   Chapter 20, Problem 8P

Chapter
Section
Textbook Problem

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.

To determine
The induced emf with in a circle of tissue of radius 1.6mm and that is perpendicular to the direction of the field.

Explanation

Given Info:

The device generates the magnetic field from zero to 1.5T in 120.0ms .

The area of the circle of tissue is,

A=πr2 (I)

•  r is the radius of the tissue

Formula to calculate the induced emf is,

ε=ΔϕΔt=(ΔBcosθ)AΔt=((BfBi)cosθ)AΔt (II)

• Bf is the final magnetic field
• Bi is the initial magnetic field
• θ is the angle between the magnetic field and the normal of circle of tissue
• A is the area of tissue
• Δt is the time taken for the magnetic field change

Substitute equation (I) in (II),

ε=((BfBi)cosθ)(πr2)Δt

Since the circle of tissue is perpendicular to the direction of field, θ=0

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