Question

In magnetic resonance imaging (MRI), a patient lies in a strong 1- to 2-TT magnetic field B⃗ B→ oriented parallel to the body. This field is produced by a large superconducting solenoid. The MRI measurements depend on the magnetic dipole moment μ⃗ μ→ of a proton, the nucleus of a hydrogen atom. The proton magnetic dipoles can have only two orientations: either with the field or against the field. The energy needed to reverse this orientation ("flip" the protons) from with the field to against the field is exactly ΔU=2μBΔU=2μB (like the energy needed to turn a compass needle from north to south).
The pulse of a radio frequency probe field irradiates the patient's body in the region to be imaged. If this probe field is tuned correctly so that its energy equals the ΔU=2μBΔU=2μB needed to reverse the orientation of the protons from with the external BB field to against it, a reasonable number of protons will flip. When the protons return to their initial orientation and a lower energy state, they emit this same radio frequency radiation in different directions. This radiation is detected and provides a measure of the concentration of protons in the region irradiated by the probe field. The proton concentration differs in fat, muscle, and bone tissue, and in healthy and diseased tissue. Thus, the probe signal makes an image of the tissue type in each local region.
The MRI image of an internal body part is made by adjusting an auxiliary magnetic field, which varies the external BB field over the region being examined so that the probe field energy equals the flipping energy ΔU=2μBΔU=2μB in only a small area of the body. A measurement is made at that point. The external magnetic field is then adjusted to flip protons in a neighboring small area of the body. Continual shifts in the magnetic field and detection of proton concentrations at different tiny locations produce a map of proton concentration in the body. The MRI image of the lower back in the figure indicates an L45 disk that has partially collapsed-it has lost water and because it contains fewer protons produces a darker MRI image.

The energy of the probe field causes protons to flip when in a 1.50-TT magnetic field. A ±± 1.30×10⁻³-TT variation in the magnetic field causes a mismatch with the radio frequency flipping field and no flipping at a distance of 2.30×10⁻³ mm from where the magnetic field is matched to the flipping field. Determine the change in the BB field per unit distance.

Express your answer in teslas per meter.

Answer 1