A metal loop of radius 0.20 m and resistance 0.14 Ohm lies in the magnetic field

Question

A metal loop of radius 0.20 m and resistance 0.14 Ohm 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 0.15 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

The emf is E = m . For a constant area, oriented along the direction of the magnetic field, then m = AB. (A=area and B= magnetic field)

So, m = AB A B t . So, the amount of time, t AB E .

give t = AB E = (pi * r^2) * B * E

E = I * R= 0.15 * 0.14 =0.021V

t = 3.14 *0.2^2 * 3 * 0.021 = 7.913 x 10-3 = 7.913 msec

. So, we should turn the magnetic field on or off over a time interval longer than 3 seconds.

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