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Due to electrostatic induction, when a charged object gets closer to a neutral object, sides of the neutral object can get charged. Thus, a charged object can attract a neutral object. However, is there a way to determine how strong would that attraction be? Can all the free electrons of a neutral object can gather on a side? If so, how many Coulombs of charge can gather?

Let's say we have a charged plate with 2 Coulombs of negative charge on it and a neutral object 2 meters away from the charged plate. How can we find the electrostatic force on the neutral object due to the charged object? I think while the one side of the neutral object attracts the charged object, the other side repels so the net force wouldn't be so much if the neutral object distance between the one side to the other is not so great.

Moreover, what would be the effect of the charged plate on a handheld electronic device or human body? Would these devices or our body get affected differently than a normal neutral object?

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Too many questions inside one question!!! And from your questions it's not even clear how much of the mathematics you will understand, no offence. So I won't be giving you any rigorous answer, I'll just point out where you might get answers.

Yes there is a way to determine these things. It's given by a combination of Electric Displacement Field, Polarization Densities and Electric Fields. But first of all you need to understand electric dipole moment, dielectric and permittivity and the difference between dielectrics and conductors.

Good Luck.

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Suppose we have a positively charged sphere in vacuum and another neutral sphere. The charged sphere creates an electric field. This field will be identical with that of a point charge. The field varies as inverse square of distance. The neutral sphere feels like it is placed in a uniform electric field that has a value same as that at the point due to the charged sphere. This electric field presence induces some charge on the left side of neutral sphere. The negative charges are pushed to the left side. This induces an electric field on the neutral sphere. But the electric field cannot penetrate through the sphere as it will violate Gauss's law. So the neutral sphere becomes oppositely charged that will produce an electric field that could counterbalance the incoming electric field at that point. This is to maintain an electrostatic equilibrium between the two spheres.

Whether positive or negative the charge, it will attract a neutral object.

Now if you need to find the induced charge on the neutral sphere, find the electric field due to charged sphere at the distance where the neutral sphere is located. We assume that the radius of the neutral sphere is very less compared to the distance of separation between the two spheres. Then you will get the electric field acting on the neutral sphere. Let's assume that our spheres are in vacuum. Then this electric field will be equal to the electric field developed by the neutral sphere as required by electrostatic equilibrium condition. The induced electric field will be opposite to the field at that point. From that value, and by using the electric field equation of a charged sphere, you can determine the charge on the neutral sphere.

When a charged object is placed near human, he will feel goosebumps. It is because, say, a positive charge is place near you. You are grounded. So since human body is a conductor, it carries negative charge from the ground to counteract that electric field. If you make contact with the charged object, the entire charge floes to the ground and the object becomes neutral.

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