By now, in most places around the world there are laws in place to mandate a minimum efficiency for power supplies. To achieve the mandated efficiency, manufacturers use so-called switching power supplies, which are based on quickly switching electronic switches on and off and using the energy "storage" characteristics of coils (current) and capacitors (voltage). Under certain circumstances, those switching frequencies or harmonics thereof (harmonics=base frequency multiplied by a whole number, but sometimes also divided) fall into the audible range. The magnetic fields changing over time cause forces changing over time on the metal loops of the coil, making them want to move in sync. If nothing prevents them from moving and if, by moving, they somehow hit each other or are massive enough to move enough air to be heard, you get the whine. Sometimes capacitors can also whine because of something called piezoelectric effect.

It can be alleviated by careful choice of switching frequency and coils and capacitors, although perfect silence in all conditions often isn't a top priority in design. Coating the coil can also help, but the used material needs to be as transparent as possible to the magnetic field and could inversely affect thermal dissipation.

Coil whine is a high-pitched noise that is caused by electrical current flowing through the coils of a laptop's power supply. It is usually caused by components vibrating due to the current and can be heard when the laptop is in use. It is often caused by poor manufacturing and design, as components can be poorly soldered or not properly secured. It can also be caused by components running at higher frequencies than they were designed for. To reduce coil whine, it is important to ensure that components are properly secured and that the laptop is running at the manufacturer's recommended frequencies. It is also important to ensure that the power supply is of good quality and that the laptop is running at the correct voltage.

It's a blanket term for all EM-induced vibrations that lead to audible noise, and generally yeah it's something you either want to avoid or mitigate with sound dampening materials.

When you run a current through a wire it creates a magnetic field. Flip that current on and off real quick and you'll get a vibrating wire. Coil that wire up real tight to make an inductor and now you've got a thing vibrating at a high frequency and possibly having an audible frequency getting kicked off

Coils vibrate, it's just what they do. Normally they're running at hundreds of kilohertz to megahertz so it's way beyond audible range but sometimes it makes the core rattle at an audible frequency, but it's hard to fix by winding differently

Common solutions are a big dollop of hot glue(yeah, just normal hot glue, it's cheap) or dipping the coil/transformer in varnish (clear nail polish). Both solutions just bind things together better so they can't move/vibrate as well

The company I worked for had designed all of our PCBs, (printed circuit boards) using switch mode power supplies without integrated components. Essentially, we had to add the coil, capacitors, resistors, etc… to define the characteristics of the supply. It just so happened the parts we selected caused the frequency the system operated at to be in the audible range. It caused an audible hum or whine, when operating.

To alleviate our issues, we selected different values of components that in the end achieved the same output characteristics, but at a higher operating frequency to prevent the hum. Pretty minor fix and everything else was the same except for the operating frequency so the hum was gone.