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 2.2-cm-diameter wedding band is parallel to the field.

Part A

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

Express your answer to two significant figures and include the appropriate units.

Part B

If the band is made of a gold alloy with resistivity6.2×108m and has a cross-section area 4.3 mm2 , what is the induced current?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A)From Faradays law of electromagnetic induction, the emf induced in the ring will be given by

emf = -d(phi)/dt

emf = -d(BA)/dt = -A dB/dt = A (B2 - B1)/t

emf = pi r^2 (B2 - B1)/t

emf = 3.14 x (0.022/2)^2 (2.5 - 0)/200 x 10^-6 = 4.75 Volts

Hence, induced emf = 4.75 volts

b)We know that resistance is given by

R = rho L/A

L = 2 pi r = 2 x 3.14 x 0.011 = 0.069 m

R = 6.2 x 10^-8 x 0.069 m / 4.3 x 10^-6 = 9.95 x 10^-4 m

i = v/R = 4.75/9.95 x 10^-4 = 4.77 x 10^3 A

Hence, i = 4.77 x 10^3 A

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