Discuss the theory of the following methods used for the measurement of magnetic susceptibility: (a) Faraday's method (b) Evan's method

Magnetic susceptibility, represented by the Greek letter chi \(\chi\), is a measure of how much a material will become magnetized in an applied magnetic field. Faraday's method is one of the prominent methods for measuring \(\chi\). \n\nIn Faraday's method, a sample (either liquid or solid) is placed within a primary coil through which an alternating current is passed to create a magnetic field variable with time. The magnetization \(\mathbf{M}\) of the sample induces an electric field, creating a current in the secondary coil. This induced current is proportional to the rate of change of magnetic flux, which is in turn dependent on the magnetic susceptibility of the material. By measuring the induced voltage, the magnetic susceptibility can be calculated.

Another method for measuring magnetic susceptibility is the Evan's method. Unlike Faraday's method, which is most useful for diamagnetic and paramagnetic substances, the Evan's method is appropriate for compounds that exhibit relatively high magnetic susceptibilities. \n\nEvan's method involves dissolving the sample in a solvent and then placing it in a NMR tube, which is placed between two strong magnets. The magnetic field affects the electronic spins in the sample and causes them to resonate at a frequency the is relayed and detected in the spectrometer. This detected resonance, known as the chemical shift, is a unique property of an atom in a molecule, and its measurement allows for the determination of the magnetic susceptibility.