# Problem: 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 μs . 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.Part AWhat emf is induced in the ring as the field changes?Express your answer to two significant figures and include the appropriate units.ε = ___________Part BIf 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 x 1010 Ω•m.Express your answer to two significant figures and include the appropriate units.I = ____________

###### FREE Expert Solution

The emf induced in the ring as the field changes is expressed as:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}\frac{\mathbf{-}\mathbf{N}{\mathbf{\pi r}}^{\mathbf{2}}\mathbf{∆}\mathbf{B}}{\mathbf{∆}\mathbf{t}}}$ where ε is the emf induced in the ring as the magnetic field changes, is the number of turns, ΔB is the change in the magnetic field, r is the radius of the circular ring, and Δt is the time interval.

The resistance of the wedding band is given by:

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{\mathbf{\rho }\mathbf{L}}{\mathbf{A}}}$, where ρ is the resistivity of the band, is the length of the band, and is the area of the band.

The length of the wedding band is:

$\overline{){\mathbf{L}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi r}}}$, where is the radius of the band.

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###### Problem Details

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 μs . 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.

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.
ε = ___________

Part B
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 x 1010 Ω•m.
Express your answer to two significant figures and include the appropriate units.
I = ____________

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