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 μs. 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 with the appropriate units.

Part B- If the band is made of a gold alloy with resistivity 6.2×10−8Ω⋅m and has a cross-section area 4.5 mm2, what is the induced current? Express your answer with the appropriate units

Answer 1

we have a circular loop of diameter 2.3 cm, whose plane is perpendicular to magneti field applied.

Given :

r = radius of loop 2.3/2 = 0.0115 m

magnetic field changes from 0 to 2.5 T in time 200 micro second.

Area of loop =

a) E.m.f induced in the loop = change of flux / time interval

b) Resistivity of loop = = 6.2 x 10-8 ohm m

cross-section area of the band = A = 4.5 mm2 = 4.5 x 10-6 m2 .

length of band = l = 2r = 2 x x 0.0115 = 0.072 m

Resistance = .

current induced is = E.m.f / R = 5.19 / 0.00099 = 5242.42 A. [Answer]