I do not understand one concept in Physics: why charged objects (eg. a charged rod or comb) attract pieces of paper when brought close to them, but do not attract pieces of metal.
I know that the pieces of paper are being polarized. But don't the pieces of metal have a sea of electrons which can move about, hence forming an electric field between the charged object and the metal?
Hope my doubt will be clarified.
Thanks
Best Answer
You can attract metal with static electricity. Consider the text-book example of a conducting sphere vs. a dielectric sphere in an electric field.
Let's assume the field is homogeneous. This field polarizes both spheres, but in different ways:
The net force on the spheres inside a homogeneous field is of course zero, because dipoles aren't attracted by homogeneous fields: The forces on the positively charged regions cancel the forces on the negatively charged regions, except for maybe a torque on the dipole. Since the dipole of the conducting sphere or the dielectric sphere is induced, the dipole is already aligned, so there is no torque.
Dipoles are instead attracted by the change of the electric field. Mathematically speaking, the force is given by $\vec{F} = \vec{\nabla} (\vec{p}\vec{E})$. Because the induced dipole self-aligns with the external field, this always pulls the spheres into the field.
To calculate the force that a nonhomogeneous field exerts on our conducting or dielectric sphere, you could try to decompose the field into an "average" homogeneous field that induces a dipole + an inhomogeneous field that pulls on the dipole. But that only works for inhomogeneities that are small across the sphere, when compared to the main field.
The conducting vs. dielectric sphere model is only a toy model, but it shows that metal is actually attracted more strongly by static electric fields than paper, because its charges can move more freely.
Below is a very non-scientific experiment to show that metal is attracted by static electricity. It uses a small Van de Graaff generator that is built-into a "magic stick" and sold as a toy. (These are fun to play around with and also useful for science demonstrations. I highly recommend this type of toy, but I have no experience with the specific product that I linked to.)
However, since electrons are free to move inside the metal, there are some practical differenes between using paper flakes and small pieces of metal:
Here is a quick try with the "magic wand" and paper (standard 80g/m^2, which is a bit too heavy). Ballpoint pen for scale, and for my cell-phone-camera to focus on.
Here is mylar foil, for comparison:
I used a piece of paper as the bottom surface, because it can actually accept charges from the metal pieces. This avoids the problem of the clinginess of the metal pieces. However, the paper surface charges up and repels the metal pieces again, and you get a very pronounced boune-back-and-forth effect. As the paper surface gets more and more charged, the mylar pieces move more and more out. You can see this a bit more clearly in the longer video. Note how the metal pieces move away from the paper, but cling to the table.
I have to admit that I am not entirely sure I understand the clinginess phenomenon. I think it is a complicated mix of the triboelectric series, grounded planes with isolated surfaces, and induced dipoles in the mylar film. But in my experience this is typical for electrostatics: Any real world application of electrostatics is about an order of magnitude more difficult than you initially think.