Physics 

The orientation of a proton's magnetic north is described probabilistically. Under normal circumstances, this probability is evenly distributed. This means that the combined magnetic field of many hydrogen atoms cancel out. When protons are inserted in a large external magnetic field, the distribution of the magnets changes, aligning them with the external field. Now, the spins want to align themselves back to their original position, but they don’t fall back immediately, and decay in a spiraling motion. This decay causes a changing magnetic field, and by placing a coil of wire nearby, the current can be measured. 

Higher magnetic fields require higher electric currents, but this would melt ordinary wires. For this reason, superconducting coils are used. 

The resistance of a superconducting coil is zero at zero Kelvin. This means that an electric current travels in a loop of superconducting material indefinitely, never needing a power source. The main consumption of energy in an MRI isn't therefore for due to the electric current,  but due to keeping the coil cooled down. The current will travel endlessly, leaving the MRI magnet permanently on. To achieve the necessary  cold temperature, liquid helium is placed in  vacuum-sealed chambers to prevent evaporation. 

To find the physical location of the hydrogen atoms, one looks at the decay of the Hydrogen protons. The spiral decay pattern of hydrogen has a unique rotational frequency (omega), that depends on the magnetic field strength. Atoms in a stronger magnetic field will rotate faster and vice versa. 

To image individual slices, one can apply a gradient to the magnetic field strength and selectively nudge atoms along the gradient by applying the corresponding frequency. This gradient is applied by using a separate set of regular electromagnets, named gradient coils. To image a slice near the weaker end of the tube, the machine sends a pulse centered at lower rotational frequencies. Whilst for slices near the stronger end, higher rotational frequencies are applied (the difference lies around 1 MHz).

T1 and T2 times

Analysis 

In 1822, Joseph Fourier developed a mathematical framework (Fourier transformation) to decompose complex waves into simpler ones. 

Any image can be deconstructed into a weighted average of simpler black and white stripes. This is what MRIs use to create images. Instead of focusing on individual pixels, different striped patterns are sampled. 

By turning on gradients in the Y and X direction, MRI can create patterns in all directions and frequencies. The machine imprints patterns with different frequencies and orientations, measures their relative strengths, and constructs an image. This is what forms the image for each 2D slice and is done for every slice of the body. 

Physics - In detail 

For the detailed physics I have added a document as there were too many formulas for a web page. The content is very detailed and often complicated for beginners, I suggest to look at the videos in the reference to have a more clear overview. 

Table of Contents of document

MRI physics – details

MRI components

The detected signal equation

Spin dynamics (T1, T2, TE, TR)

Polarization

Boltzmann Magnetization

NMR Experiment Transmission (Tx) and Reception (Rx)

Dephasing

Spin Echo experiment

Total scan time

Pulse and Magnetic gradient

Gradient Echo (GRE) – Detailed explanation

Gradient Echo (GRE) vs Spin Echo