In many developing countries (I live in one in Asia), there is no earthing/grounding of the power lines in the house/street/city.
The result is that if I touch my laptop I often feel that is has a potential voltage difference (It gives you a little shock, also introducing humming noises in headsets connected via USB port, electric guitars, too)
I have two question:
If you connect an Arduino to a laptop that is not grounded, does that mean the Arduino is also not grounded, therefore possibly creating unwanted signal noise or even damage.
How is an Arduino board grounded say when connected to a USB power bank or anything really like batteries or solar cells.
A laptop powered from the charger/adapter often has no connection to earth ground. That terminates in the adapter, and the DC power that goes to the laptop is isolated from earth ground.
Desktops are different, usually the earth ground supplied to the unit, continues from the power supply to the entire frame and motherboard.
There is a "ground" but it's just a "common" or "return" or "reference" and not earth-ground. (A USB power bank might sometimes have an earth ground.) Your car is similar - The car body is considered "ground" and it's connected to the negative battery terminal but obviously the tires are insulated so there is no earth ground.
Scary and strange! Is that normal where you live? Is one of the power wires "neutral"? Here in the U.S., most power outlets have 2 "power connections" and a ground but some power plugs don't have the ground. There are 2 things that make that "safe". Usually the item is "double insulated" which means there is no ground but user is insulated from the voltage.
A desktop computer does normally have an earth ground through the power-cord connection (in most countries). But, that ground is completely isolated from the AC power so if that earth-ground is cut, it's still safe... as long as there is no fault.
There other safety feature is that one of the power-wires is "neutral" and connected to ground at the circuit-breaker box. The plug is polarized (one plug-blade is larger than the other) and on some older products the the neutral is connected to the chassis. This can be dangerous if the wires are reversed, or if a non-polarized extension cord is used, so they don't sell those things anymore. (If you get a shock you can turn the plug over to reverse the connections.)
In a lamp the screw-part of the bulb is connected to neutral so you have to stick your finger all the way in to get a shock. (If everything is wired right!)
Usually, a laptop's power supply is transformer-isolated so there is normally no direct-connection to the AC power or AC/earth ground. There is a often a ground on the AC side, but that's usually not connected to "ground" on the DC side. You can check that if you have an Ohmmeter and/or you might want to try a different power supply/charger. But, if you plug something into the laptop with it's own power supply, there can be a connection (hopefully to earth ground).
It won't be grounded unless it has it's own-separate ground. The "floating ground" can provide noise shielding if you have shielded cable or a metal box, etc. Normally, the Arduino (and you!) are safe, but if you are getting a shock I'd say neither you or the Arduino is safe!
It's not dangerous to have a floating ground unless that floating-ground is "energized."
Normally, a "safety ground" works like this - If there is a fault that puts voltage on the ground (say, your computer case or a metal box containing your Arduino), that voltage is "shorted to ground" so you cant' get a shock if you touch the box and ground at the same time, and a circuit breaker will be tripped turning-off the power.
Part of the problem here is terminology, there are 3 terms: Earth, Ground and 0V that are used interchangeably as if they mean the same thing. Not only do they not mean the same thing, I get the impression, not verified, that earth and ground do not mean the same thing in different parts of the English speaking world. What they mean in parts of the world where English is not the primary language I do not know.
Those terms are used interchangeably because they are often connected together so one connection ends up doing different but related things. I am hesitating to explain more because when I wrote the common ground tutorial I decided it was going to be difficult to get it right and it was well beyond the scope of the problem I was trying to address.
Your lack of electrical earth from the supply is a safety issue not an issue for the functioning of the circuit although it might be an issue for the continued functioning of your body given the safety implications. You are already getting shocks, be careful!
I started typing the above before @DVDdoug posted reply #5 , but his reply was there by the time I'd finished. He explanation of the US system adds to my reluctance to define earth, ground and 0V. The US system is different to the UK system, although there are some similarities and both are trying to achieve safety.
You are not alone!
In Highschool, there was a bunch of technical oriented guys who ran the film and slide projectors for various teachers. One of my friends, Joe, could not do it because he felt the AC on the device components, no matter which one or what type, as long as it was plugged into the mains power. No one else ever had a problem.