A solution to RWP2 - MRI Health and Safety

The primary safety concern regarding the strong static magnetic field generated by an MR system is that ferromagnetic objects may be attracted to the magnet with a force that is much greater than their weight, and a person could be injured or killed if they are in the path of the projectile.  The magnetic force of attraction on a ferromagnetic object (like a steel button) depends on the strength and divergence of the magnetic field at the position of the object, as well as the size of the object.  If the magnetic field is uniform (like in the center of the MR solenoid), then there is no net force on the object since the magnetic force on each of the induced magnetic poles are equal and opposite.  However, near the edges of the solenoid, the magnetic field lines diverge (spread out) significantly, so the end of the object that is closest to the magnet is attracted with a force that is significantly greater than the repulsive force acting on the induced opposite pole that is farther from the solenoid.  This effect was demonstrated in class with a Helmholtz coil pair and a paper clip suspended from a string.

While we do not have an equation to use for determining the magnetic force on a ferromagnetic object, we can use our everday experience and proportional reasoning to estimate the force on a steel button.  From the demonstration shown in class with the paper clip, we saw that when the paper clip was near the edge of one coil, it was attracted to the coil with a force that was approximately equal to its weight since the string made an angle of approximately 45 degrees from vertical.  We recall that the current through the coils was about 2 A, which as we learned from the e/m lab, creates a magnetic field of about 50 G, which is about 100 times stronger than the earth's magnetic field.  Since the magnetic field from an MR system is about 1.5 T or 15 kG, the magnetic force on a button near the opening would be about 300 times its weight.  Assuming the button has a mass of about 5 g (the same as a nickel coin), then this would mean that the magnetic force on it near the opening of an active MRI system would be about 15 N or 3 lbs.  If the button moved closer to the edge of the MR magnet, the force of attraction would increase significantly.  We could estimate this maximum force by knowing that a small refrigerator magnet (typically 10 G near its poles) can easily support its own weight, so a powerful MR magnet that is 1500 times stronger, could exert a maximum force on a ferromagnetic object that is at least 1500 times more than the weight of the object!  This means that the attractive force on a button near the edge of an activated MR solenoid could be as much as 75 N or 15 lbs.  While this may not seem like a large force, just imagine how much greater the force would be on a more massive object like an oxygen tank that weighs 10 lbs.  The magnetic attractive force could be as much as 10 000 lbs, enough to kill a person - as was the case in one such instance (Ref. 1).

The other primary concern related to the magnetic fields associated with an MRI is that large currents can be induced in metal objects (not just ferromagnetic materials), and these currents can make the metal very hot.  For example, if a patient wore a gold necklace during an MRI scan, the changing magnetic field (slew rate of ~50 T/m/s) could induce an emf in the necklace that is approximately:
    emf = d(Phi)/dt = Area*slew ~ (0.02 m^2)(50 T/s) = 1 V
While this induced emf may not seem large, it is important to remember that the resistance of the conductor is very small (~0.001 ohm - see sample calculation below), in which case the induced current would be 1000 A, and the power dissipated by resistive heating would be:  P = IV = 1000 W.  This electrical power is similar to that of a toaster, and could easily result in a severe skin burn! (Ref.2)  Potentially harmful currents could also be induced in conductors worn by a medical assistant near the magnet if there was a changing magnetic flux (either due to a change in the magnetic field or the orientation of the conductor).  Since the magnetic field outside the solenoid is much less than inside, the burn risk is signficantly lower, but could still be a concern.

Approximate resistance of gold necklace:
Resistivity of gold:  r = 2.2e-8 ohm-m
Length of necklace:  L = 18 in = 45 cm
Cross-sectional area:  A = pi*(0.002 m)^2 = 1.2e-5 m^2
R = rL/A = 0.0008 ohm

Other insights and bad physics on the web:

One of the websites listed as a reference (Ref.3) for this problem has a diagram with an equation for the attractive force on an object:  F = m/d^2, but this equation cannot possibly be correct since the units on the right are not those of a force.  This equation also does not include the strength of the magnetic field and its divergence, both of which are necessary for computing the attractive force.  The force of attraction also depends more on the size and magnetic susceptibility of the object than on its mass.  This same website also has a diagram for the 5 G fringe field that surrounds a magnet, but the mangetic field lines shown are not consistent with those of a dipole that has a stronger field near the poles than the center.

Examination of the health effects due to the strong magnetic fields from an MR system elicits questions about the efficacy of magnetic therapies that are widely marketed today.  Numerous claims have been made that magnets placed near the skin can stimulate circulation in the body and heal relieve aches and pains, but not scientific studies have been able to verify these claims or explain how such processes are possible.  Many of the statements made by magnet therapy vendors are inconsistent with the laws of physics; however, there have been studies that validate the placebo effect that can occur when patients believe in the efficacy of a therapy, even if there is no scientific reason for there to be a healing effect. (Ref.4)

References:
1)  http://www.fda.gov/cdrh/safety/mrisafety.html
2)  http://www.massgeneralimaging.org/newsletter
3)  http://www.erads.com/mrsafety.htm
4)  http://skepdic.com/magnetic.html

Grading rubric: (10 pts. total)
4 - overall quality of essay, correct physics, proper justification of statements, citation of sources used
2 - effects on ferromagnetic materials, including calculations (magnetic attractive force, projectiles)
2 - effects on non-ferromagnetic materials, including calculations (induced currents, skin burns)
2 - other insights (biological currents, magnet therapy, bad physics on the web, etc.)