Final answer:
The coil for a gradient echo in an MRI is integrated into the MRI machine and used alongside a cylindrical solenoid to create a varying magnetic field that facilitates the imaging process.
Step-by-step explanation:
The coil used for a gradient echo in magnetic resonance imaging (MRI) is oriented within the MRI machine in such a way as to produce variations in the main magnetic field. This spatial variation allows for the encoding of position information into the signal, which is necessary for creating the image. In an MRI machine, a large magnetic field is generated by a cylindrical solenoid surrounding the patient. The patient lies down on a table that slides into the center of this solenoid. Additionally, gradient coils are used to create a gradient echo by varying the magnetic field across the sample, which assigns different resonant frequencies to protons at different locations within the body. Broadcasting radio frequencies across a range and the subsequent reemission of these frequencies by the protons allows for the creation of a detailed tissue map of the body.