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

Answer 1

Explanation:

It is given that, the field near a typical pulsed-field machine rises from 0 T to 2.5 T in 200 μs

Change in magnetic field, $dB=2.5\ T$

Change in time, $dt=200\ \mu s=200\times 10^{-6}\ s=2\times 10^{-4}\ s$

Diameter, d = 2.3 cm

Radius, r = 0.0115 m

Emf is induced in the ring as the field changes. It is given by :

$E=\dfrac{d\phi}{dt}$

$E=\dfrac{d(B.A\ cos(0))}{dt}$

$E=A\dfrac{d(B)}{dt}$

$E=\pi (0.0115)^2\dfrac{2.5}{2\times 10^{-4}}$

E = 5.19 volts

So, the emf induced in the ring is 5.19 volts. Hence, this is the required solution.