# How is current induced in the coil in NMR?

In nuclear magnetic resonance some current is indeced in the receiving coin by the rotating magnetisation vector. The current is associated with some energy. From where this energy come from since there is no energy transfer between object and the coil? Or maybe there is?

## 1 Answer

In NMR there are two magnetic fields of importance:

1. the permanent field

2. the sinusoidal/pulsed field

The permanent field results in a macroscopic magnetization vector in the object being studied where the potential energy of the system is at a minimum for the particular geometry of the object/field/surroundings.

The sinusoidal or pulsed field is oriented perpendicular to the permanent field and causes the net magnetization to rotate to some angle, $0 < \theta \le \pi$ with respect to the permanent field direction by inputting energy to the system. When the magnetization is not aligned with the permanent magnet, the system has potential energy higher than its minimum. The angle to which it orients depends on the chemistry of the object, the strengths of the fields, and the frequency and length of the pulse applied.

When the pulse is turned off, the net magnetization will decay back to a zero angle, losing energy in the process and inducing a current in the pickup coil (due to a net changing magnetic field).

There is a whole variety of timing factors (T1, T2, chemical shifts, FFT) which can be measured, tuned, analyzed which will give different types of information to scientists, engineers, and physicians depending on what they wish to study.

This e-book is a great starting point for looking into NMR.

• The energy which induce the current in the receiving coil comes from the difference between the equilibrium and excitated states? Did I understood correctly? So, what if (in theory) the T1 and T2 times are equal to infinity? the signal will be generated forever, but at the cost of what energy? Jun 3, 2017 at 15:12
• T1 and T2 times are mean decay times. The longer they are the smaller the power (energy per time). It's impossible (in theory) for them to be infinite because there is only a finite potential energy difference. If (mathematically) you make them infinite, there is no induced current because there is no decay back to the equilibrium state. It's the change in the magnetic field that induces the current. Jun 3, 2017 at 15:33
• If relaxation times are mathematically infinite, there is no relaxation, however, after excitation there is a change in the magnetic field, because the magnetisation vector is rotating in xy plane. So, why there is no induced current? Jun 4, 2017 at 13:07
• @KarolBorkowski - Faraday's Law. There would be no change in the flux through the pickup coil oriented in the x-y plane. Jun 4, 2017 at 13:43
• According to Faraday's Law if the coil is rotating relative to the magnetic field, a voltage is induced. The magnetisation vector is rotating so the magnetic field is doing so. Where I make a mistake? Jun 5, 2017 at 17:09