There are many electronics inside a laptop that can create high pitches squeal noises. I'm not an expert electrician but one of the more often thought reasons for this is that some (presumably cheap) capacitors (electronic device that can store electricity for a short period of time, a capacitor is like a slow leaking buffer of electricity) emit sound when current flows through them. It's probably because they're fed some weird square-wave alternating voltage. That's all I can think of. :\
While not many people can hear such high pitched noises (actually, I've never met anyone that can hear the noises I hear and I even had them listen with their ears on the device and they didn't hear anything), I can.
On my laptop, these noises have two triggers: one is unplugging the power jack from the laptop and the other one, which I've just discovered, is caused by AMD/ATI's PowerPlay battery/energy-saving technology.
Unplugging the power jack doesn't create much noise. It's a bearable lower-high pitched noise that seems to go away after a while, although it immediately stops when I plug the jack back in.
But when AMD/ATI's PowerPlay is turned off or it's set to Maximum Performance (ie. no throttling), my laptop starts making this annoying high pitched noise that modulates slightly with moving the mouse cursor and more if I move a window on the screen. Turning PowerPlay off doesn't help. Turning it on and setting it to Maximum Battery however, completely stops any squealing or any other high pitched noise. What does this mean? Poorly manufactured device? My laptop is a Sony Vaio VPC-EB2S1E, though. I don't know what to say. :\
This is the only fix I know of so far and I found it myself by accident. I hope this helps, unless you play games or like desktop effects and desktop compositing to be snappy...
Here's a screenshot of the Catalyst Control Center: