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 us. 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. A)What emf is induced in the ring as the field changes? Express your answer to two significant figures and include the appropriate units. B)If the band is gold with a cross-section area of 4.0 mm^2 , what is the induced current? Assume the band is of jeweler's gold and its resistivity is 13.2*10^-10 ohm*m. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The induced emf in the ring will be approximately (CSA of loop) x dB/dt = pi x (0.01m)^2 x (2.5 - 0)T / 200e-6 s = 3.93V The end-to-end resistance of the ring before being joined at the ends is R = resistivity x length / c.s area. (length = circumference of ring here) R = 13.2e-10 x pi x 0.02m / 4e-6 m^2 R = 20.7 micro-ohm The loop resistance after joing at the ends is 1/4 of this value (2 half-lengths in parallel) R = 5.18 micro-ohm Hence, current induced in the ring is I = V/R = 3.93V/5.18 micro-ohm = 0.757MA = 757,000 Amps

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