A TMS (transcranial magnetic stimulation) device creates very rapidly changing m

Question

A TMS (transcranial magnetic stimulation) device creates very rapidly changing magnetic fields. The field near a typical pulsed-field machine rises from 0 T to 2.5 T in 200 mu s. Suppose a technician holds his hand near the device so that the axis of his 2.0-cm-diameter wedding band is parallel to the field. What emf is induced in the ring as the field changes? Express your answer to two significant figures and include the appropriate units. If the band is made of a gold alloy with resistivity 6.2 times 10^-8 Ohm middot m and has a cross-section area 4.3 mm^2, what is the induced current? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

(A) flux = B A

induced emf = d(flux)/dt = A dB/dt

A = pi 0.01^2 = 3.14 x 10^-4 m^2

e = (3.14 x 10^-4) (2.5) / (200x 10^-6)

e = 3.93 Volt

(B) R = rho L / A

and L = 2 pi r =2 x pi x 0.01 = 0.0628 m

R = (6.2 x 10^-8) (0.0628) / (4.3 x 10^-6)

R = 9.06 x 10^-4 Ohm

I = e / R = 4338 A

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