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?
In NMR there are two magnetic fields of importance:
the permanent field
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.