2. A recently developed method to study brain function is to produce a rapidly c

Question

2. A recently developed method to study brain function is to produce a rapidly changing magnetic field within the brain. When this technique, known as transcranial magnetic stimulation (TMS), is applied to the prefrontal cortex, for example, it can reduce a person's ability to conjugate verbs, though other thought processes are unaffected. The rapidly varying magnetic field is produced with a circular coil of 21 turns and a radius of 6.0cm placed directly on the head of the patient. The current in this loop increases at the rate of 1.2x10^7 A/s (by discharging a capacitor). a. At what rate does the magnetic field at the center of the coil increase? (What is delta B/delta t?) b. Suppose a second coil with half the area of the first coil is used instead. Would your answer to part (a) increase, decrease, or stay the same? By what factor? c. Back to the original coil. At what rate is the magnetic flux through the center of the ring increasing? (What is delta Rho/delta t?)

Explanation / Answer

a) knowing that

B = Uoi / (2r)

so

dB/dt = (Uo /2r) di/dt = (2pi x 10^-7 x 1.2 x 10^7) / 0.06

=> dB/dt = 125.66 T/s

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b) A2 = 0.5 A1 = 0.5 (pi r^2)

so pi r2^2 = 0.5pi r^2

so r2 = r / sqrt(2)

so dB/dt (new) = sqrt(2) * dB/dt (old)

so increased by factor of sqrt(2)

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c) dphi / dt = A dB/dt = pi r^2 dB/dt

= pi (0.06)^2 * 125.66 = 1.42 w/s

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