Question

In many magnetic resonance imaging (MRI) systems, the magnetic field is produced by a superconducting magnet that must be kept cooled below the superconducting transition temperature. If the cryogenic cooling system fails, the magnet coils may lose their superconductivity and the strength of the magnetic field will rapidly decrease, or quench. The dissipation of energy as heat in the now-nonsuperconducting magnet coils can cause a rapid boil-off of the cryogenic liquid (usually liquid helium) that is used for cooling. Consider a superconducting MRI magnet for which the magnetic field decreases from 7.0 T to nearly 0 in20 s.

What is the average emf induced in a circular wedding ring of diameter 2.2 cm if the ring is at the center of the MRI magnet coils and the original magnetic field is perpendicular to the plane that is encircled by the ring?

emf = V

Answer 1

0.000133046 V

Step-by-step explanation:

B = Magnetic field = 7 T

t = Time = 20 s

d = Diameter = 2.2 cm

r = Radius =
`(d)/(2)=(2.2)/(2)=1.1\ cm`

A = Area =
`\pi r^2`

Induced emf is given by

`\epsilon=NA(dB)/(dt)\\\Rightarrow \epsilon=(1* \pi (1.1* 10^(-2))^2* 7)/(20)\\\Rightarrow \epsilon=0.000133046\ V`

The induced emf is 0.000133046 V