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 ?s. Suppose a technician holds his hand near the device so that the axis of his 1.8-cm-diameter wedding band is parallel to the field.

What emf is induced in the ring as the field changes?

If the band is made of a gold alloy with resistivity 6.2×10?8??m and has a cross-section area 4.3 mm2 , what is the induced current?

Answer 1

here,

change in magnetic feild , dB = 2.5 T

timne , t = 2 * 10^-4 s

diamter , d = 0.018 m

radius , r = 0.009 m

the emf induced , EMF = area * dB/dt

EMF = pi * 0.009^2 * 2.5 /( 2 * 10^-4)

EMF = 3.18 V

b)

resistivity , p = 6.2 * 10^-8 ohm.m

area , a = 4.3 * 10^-6 m^2

length ,l = 2 * pi * r

l = 2 * pi * 0.009

l = 0.05652 m

resistance , R = p * l /a

R = 6.2 * 10^-8 * 0.05652 /( 4.3 * 10^-6)

R = 8.14 * 10^-4 ohm

current , I = EMF /R

I = 3.90 * 10^3 A

the current induced is 3.90* 10^3 A