A metal loop of radius 0.26 m and resistance 0.12 lies in the magnetic field due

Question

A metal loop of radius 0.26 m and resistance 0.12 lies in the magnetic field due to an MRI machine. The field is perpendicular to the plane of the loop, and has a magnitude of 3.0 Tesla when the NMR is operating.

In designing the MRI, one needs to be careful about the currents generated when the field turns on an off.

If the maximum safe current in the loop is 0.20 Amps, what is the shortest amount of time that the magnetic field should be turned on? Assume the field increases at a constant rate, until it reaches its operating value, when the MRI is turned on.

Give your answer in seconds to at least three significant digits. You can assume the loop is stationary.

Explanation / Answer

emf induced is change in flux per unit time

flux = magnetic field *area

area=r^2=0.21237 m^2

initial flux= 3*0.21237=0.6371 weber

let it is off in t seconds

final flux=0

change in flux per unit time=0.6371/t

emf=0.6371/t

current=emf/resistance=0.6371/(t*0.12)

safe current=0.20 A

0.6371/(t*0.12)=0.2

this gives t=26.5 sec

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