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 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.

(1) What emf is induced in the ring as the field changes? Express your answer to two significant figures and include the appropriate units.

(2) If the band is gold with a cross-section area of 4.0 mm2, what is the induced current? Assume the band is of jeweler's gold and its resistivity is 13.2×1010m. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

part A :

induced emf e = N A dB/dt

A is area = pi r^2

r is radius = D/2 = 2cm/2 = 1 cm = 0.01 m

so

emf e = 1 * 3.14* 0.01* 0.01 * (2.5 -0)/(200*10^-6)

emf e = 3.92 Volts
------------------

part B:

length of the band = L = 2pir

L= 2* 3.14 * 0.01 = 0.0628 m

Resistance R = rhi L/A

R = 13.2 * 10^-10 * 0.0628/(4*10^-6)

R = 0.0000207 ohms

Induced current I= emf/R

I = 3.92/(0.0000207)

I = 189372 Amps

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