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 2.3-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 times 10^-8 Ohm middot m and has a cross-section area 3.9 mm^2, what is the induced current?

Explanation / Answer

A)

We need to us Faraday’s law of induction,

e= d/dt

e=d(BA)/dt

e=A*dB/dt

e=r2*dB/dt

e=3.14*(0.023/2)^2*2.5/0.000200

e= 5.2 V

B)

e= 5.2 V

R=*L/A

R=*2r/A

R=6.2*10^-8*(2*3.14*0.023/2)/(3.9*10^-6)

R=0.001148

I=V/R

I=5.2/0.001148

I = 4500 A

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