Problem 25.64 A TMS (transcranial magnetic stimulation) device creates very rapi

Question

Problem 25.64 A TMS (transcranial magnetic stimulation) device creates very rapidly changing magnetic fields. The field near a typical pulsed - field machine uses 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 2.3 - cm - diameter wedding band is parallel to the field. Part A What emf is induced in the ring as the field changes? Part B If the band is made of a gold alloy with resistivity 6.2 x 10^ - 8 omega.m and has a cross - section are 3.7 mm^2 , what is the induced current?

Explanation / Answer

A)
Area of the loop, A = pi*D^2/4

= pi*0.023^2/4

= 4.15*10^-4 m^2

induced emf = A*dB/dt

= 4.15*10^-4*(2.5 - 0)/(200*10^-6)

= 5.2 volts

B) Length of the wire, L = pi*D

= pi*0.023

= 0.0722 m

cross sectional area, a = 3.7 mm^2

= 3.7*10^-6 m^2

we know, R = rho*L/a

= 6.2*10^-8*0.0722/(3.7*10^-6)

= 1.2*10^-3 ohms

induced current, I = induced emf/R

= 5.2/(1.2*10^-3)

= 4333.3 A

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