Given a maximum magnetic field gradient of 40 mTm and magnet

Given a maximum magnetic field gradient of 40 mT/m and magnetic field of 3T, how homogenous must the magnet be (in parts per million) to enable a spatial resolution of 1 mm to be acquired.

Solution

The magnetic gradiant is 40mT in 1 meters

==> change in magnetic field in 1 milimeters = 40 x 10^-3 mT = 4 x 10^-5 T; ...................................(1)

let the homogeniety be y ppm ==> This means that no two points within the given resolution differ in magnetic field strength by more than y part in a million, or by no more than 3.0T x (y / 10^-6) or 3y x 10^-6T ..........................(2)

Comparing 1 and 2:-------------

3y x 10^-6 T =  4 x 10^-5 T ==> y = 13.33 ppm