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 within 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 1.8 T in 100 ms. Determine the induced emf within a circle of tissue of radius 1.5 mm and that is perpendicular to the direction of the field.
dB/dt is 1.8/100E-6
Use Lenz's law:
V=d/dt (B*area)
1.27 E-4
To determine the induced emf within the circle of tissue, we can use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the area.
The formula for calculating the induced emf is:
emf = -dΦ/dt
where emf is the induced electromotive force, dΦ is the change in magnetic flux, and dt is the change in time.
In this case, the magnetic field within the brain rises from zero to 1.8 T in 100 ms. To find the change in magnetic flux (dΦ), we need to first calculate the initial and final magnetic flux through the circle of tissue.
The magnetic flux (Φ) through a circle of radius r and perpendicular to the magnetic field can be calculated using the formula:
Φ = B * A
where B is the magnetic field strength and A is the area of the circle.
Given that the radius of the tissue circle is 1.5 mm (or 0.0015 m) and the magnetic field rises to 1.8 T, we can calculate the initial and final magnetic flux as follows:
Initial magnetic flux (Φ1) = 0 T * π * (0.0015 m)^2
Final magnetic flux (Φ2) = 1.8 T * π * (0.0015 m)^2
Now, we can calculate the change in magnetic flux (dΦ) by subtracting the initial flux from the final flux:
dΦ = Φ2 - Φ1
Next, we need to determine the change in time (dt) from the given information. In this case, the magnetic field rises from zero to 1.8 T in 100 ms, which can be converted to seconds:
dt = 100 ms * (1 s/1000 ms)
Finally, we can use the values of dΦ and dt to calculate the induced emf (emf) using the formula mentioned earlier:
emf = -dΦ/dt
Now, we can plug in the calculated values to find the induced emf within the circle of tissue.