Study of Nuclear magnetic resonance by Qaiser Siddique, Vallo Zinin and Razib Hossain.
Basics: 
Nuclear magnetic resonance builds on the physics concepts of resonance and nuclear spin(angular momentum of elementary particles of an atom). Protons, electrons, atomic nuclei, and other elementary particles have an intrinsic spin as if they were spinning on their axes.When atomic nuclei, or other charged particles, spin they become like a magnetic dipole (like a bar magnet). A nucleus, or elementary particle, possessing spin will wobble or precess when they are placed in a magnetic field. A nucleus in a magnetic field precesses at a frequency, called the Larmor frequency, which is proportional to the magnetic field.
When an atom is in a constant magnetic field, it nucleus precesses at the Larmor frequency. If in addition to the constant magnetic field, there is also a weaker perpendicular magnetic field that varies at the same frequency as the Larmor frequency for the nucleus, then the nucleus resonates. The phenomenon is called Nuclear Magnetic Resonance (NMR).[1]
Analogy:
This nuclear magnetic resonance (NMR) causes the spin of the nucleus to flip.The analogy for Earth spinning on its axis would be if Earth flipped so that the north and south poles interchanged and Earth were suddenly spinning in the opposite direction. Just as it would take considerable energy to flip Earth's spinning motion, the nucleus absorbs and emits energy as it flips its spin. With the correct electronic equipment physicists can measure the spectrum of absorbed and emitted energy.[1]
Physics of NMR:
When the nuclear magnetic moment associated with a nuclear spin is placed in an external magnetic field, the different spin states are given different magnetic potential energies. In the presence of the static magnetic field which produces a small amount of spin polarization, a radio frequency signal of the proper frequency can induce a transition between spin states. This "spin flip" places some of the spins in their higher energy state. If the radio frequency signal is then switched off, the relaxation of the spins back to the lower state produces a measurable amount of RF signal at the resonant frequency associated with the spin flip.[2]
A magnetic dipole moment (usually just called "magnetic moment") in a magnetic field will have a potential energy related to its orientation with respect to that field.[2]
Note that the electron spin magnetic moment is opposite to the electron spin while the proton spin magnetic moment is in the direction of the proton spin. The electron spin or proton spin will tend to precess around the magnetic field with a Larmor frequency. For a 1 Tesla magnetic field this Larmor frequency would be:
The Larmor frequency can be visualized classically in terms of the precession of the magnetic moment around the magnetic field, analogous to the precession of a spinning top around the gravity field. It can also be visualized quantum mechanically in terms of the quantum energy of transition between the two possible spin states for spin 1/2. [2]
Applications of NMR
- Solution structure The only method for atomic-resolution structure determination of biomacromolecules in aqueous solutions under near physiological conditions or membrane mimeric environments.
- Molecular dynamics The most powerful technique for quantifying motional properties of biomacromolecules.
- Protein folding The most powerful tool for determining the residual structures of unfolded proteins and the structures of folding intermediates.
- Ionization state The most powerful tool for determining the chemical properties of functional groups in biomacromolecules, such as the ionization states of ionizable groups at the active sites of enzymes.
- Weak intermolecular interactions Allowing weak functional interactions between macrobiomolecules (e.g., those with dissociation constants in the micromolar to millimolar range) to be studied, which is not possible with other technologies.
- Protein hydration A power tool for the detection of interior water and its interaction with biomacromolecules.
- Hydrogen bonding A unique technique for the DIRECT detection of hydrogen bonding interactions.
- Drug screening and design Particularly useful for identifying drug leads and determining the conformations of the compounds bound to enzymes, receptors, and other proteins.
- Native membrane protein Solid state NMR has the potential for determining atomic-resolution structures of domains of membrane proteins in their native membrane environments, including those with bound ligands.
- Metabolite analysis A very powerful technology for metabolite analysis.
- Chemical analysis A matured technique for chemical identification and conformational analysis of chemicals whether synthetic or natural.
Material science A powerful tool in the research of polymer chemistry and physics. [3]
NMR Spectroscopy
One common application of nuclear magnetic resonance is NMR spectroscopy. Physicists and chemists study the NMR spectrum produced by a sample of material and deduce the properties of the nuclei in the sample. This tells them what elements are in the sample.
Magnetic Resonance Imaging (MRI) 
Proton nuclear magnetic resonance (NMR) detects the presence of hydrogens (protons) by subjecting them to a large magnetic field to partially polarize the nuclear spins, then exciting the spins with properly tuned radio frequency (RF) radiation, and then detecting weak radio frequency radiation from them as they "relax" from this magnetic interaction. The frequency of this proton "signal" is proportional to the magnetic field to which they are subjected during this relaxation process. In MRI, an image of a cross-section of tissue can be made by producing a well-calibrated magnetic field gradient across the tissue so that a certain value of magnetic field can be associated with a given location in the tissue. Since the proton signal frequency is proportional to that magnetic field, a given proton signal frequency can be assigned to a location in the tissue. This provides the information to map the tissue in terms of the protons present there. Since the proton density varies with the type of tissue, a certain amount of contrast is achieved to image the organs and other tissue variations in the subject tissue.
The hydrogen spin-flip frequency is the same for all parts of the sample. Once excited by the RF signal, the hydrogens will tend to return to their lower state in a process called "relaxation" and will re-emit RF radiation at their Larmor frequency. This signal is detected as a function of time, and then is converted to signal strength as a function of frequency by means of a Fourier transformation. Since the protons in each of the active areas of the sample are subjected to the same magnetic field, they will produce the same frequency of radiation and the Fourier transform of the detected signal will have only one peak. This one peak demonstrates the presence of hydrogen atoms, but gives no information to locate them in the sample.
Information about the location of the hydrogen atoms can be obtained by adding a calibrated gradient field across the region of the sample. With an increasing magnetic field as you move to the right across the sample, the spin-flip energy and therefore the frequency of the emitted signal increases from left to right. When excited by an RF transmitter, the emitted signal contains different frequencies for the two proton concentration areas. These frequencies can be separated by means of the Fourier transform and the example gives two different regions of frequency for the two sample areas. This is the beginning of the process of locating the hydrogen atoms.[4]
Problem :
Essential University Physics Volume 2
Chapter 38 Problem 38:
An NMR spectrometer is described as a “300-MHz instrument,” meaning 300 MHz is the frequency supplied to its transmitter coil to flip the spin states of bare protons. What’s the strength of its unperturbed magnetic field?[5]
Solution:
References :
[1]- Basics and Analogy of NMR: http://suite101.com/article/understanding-nuclear-magnetic-resonance-a157340
[2]- Physics of NMR : http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html
[3]- Applications of NMR : http://www2.chemistry.msu.edu/facilities/nmr/900Mhz/MCSB_NMR_applications.html
[4]- MRI: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mri.html
[5]- Solution to problem - http://www.chegg.com
Images:
[Fig. 1] Magnetic Resonance : http://en.wikipedia.org/wiki/File:NMR_EPR.gif
[Fig. 2] Magnetic Moment: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html
[Fig. 3] Larmor frequency: http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmr.html
[Fig. 4] MRI Illustration : http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mri.html
[Fig. 5] Solution to problem - http://www.chegg.com