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 from0 T to 2.5 T in 200 ?s. Suppose a technician holds his hand near the device so that the axis of his 2.3-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 resistivity 6.2

Explanation / Answer

a) We have the formula for the induced emf is

          e = A ?B/?t

Here A = ?r^2

         r = 0.0115 m

         ?B/?t = (2.5 T -0)/(200 ?s)

                   = 1.25 x 10^4 T/s

        e =( ?r^2)( ?B/?t)

            = (? (0.0115 m)^2)(1.25 x 10^4 T/s)

            = 5.1934 V

B) The resistance of the wire is

           R = ?L /(?R^2)

The length of band is L = 2?r

                                      = 2?(0.0115 m)

                                      = 0.07226 m

             R = ( 6.2 x 10-8 ?*m)( 0.07226 m )/(4.5 x 10^-6m2)

                  =9.9558*10^-4 = 0.00099558 ?

So the induced current is

            I = e/R

              = ( 5.1934 V)/(0.00099558 ?)

              = 5216.44 A

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