A metal loop of radius 0.28 m and resistance 0.13 lies in the magnetic field due
ID: 1486496 • Letter: A
Question
A metal loop of radius 0.28 m and resistance 0.13 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 0.10 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
given
radius of the loop, r = 0.28 m
Area of the loop, A = pi*r^2
= pi*0.28^2
= 0.2463 m^2
resitnace of the loop, R = 0.13 ohms
From the given data,
maximum induced emf = maximum safe current current*R
= 0.1*0.13
= 0.013 volts
we know, induced emf = A*dB/dt
==> dt = A*dB/induced emf
= 0.2463*(3-0)/0.013
= 56.8 s <<<<<<<<<<-----------------Answer