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2

Yes. Force is a vector quantity which means it is characterized by both magnitude and direction. You don't need to know the signs of the charges to determine the magnitude of the force, but you do need to know them to determine the direction of the force (repulsive or attractive). Hope this helps.


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No we don't but if we want to find if the force is repulsive or attractive then we must take into account the type of the charges. And negative and positive charge are just conventional we use them to understand better the 2 types of electric charges and to define several helpful quantities ( potential or potential energy).


0

Yes, it is possible. If you know how to calculate the force on a poitn charge $q$ due to a continuous body... then... you have to sum up (integrate) the forces over all the $dq$s of the second body. However, this is quite difficult and it's not often done. It's quite easy to calculate the force on a charge q due to a charged circle. But the force between ...


4

Coulomb used a torsion balance to measure the force between two known charges at a known separation. Knowing the charges, the separation, and the force allows $k_e$ to be computed. Here are the details, from Wikipedia: The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. If an ...


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From mathematical perspective, your perfect field line (called separatrix) will end in a saddle point (see the picture below). However, physics doesn't talk a lot about separatrices, because any small deviation will bump the test particle either in upper or in lower half-plane.


0

It is the distance between the centers of the two spheres


1

The Coulomb force that acts on the charge $q_2$ is equal to the electric field at the position of $q_2$ multiplied with the charge $q_2$. This becomes $$F = Eq_2 = \frac{1}{4\pi \varepsilon_0 k} \frac{q_1}{ r^2} q_2$$ with $E$ the electric field, $\varepsilon_0$ the vacuum permittivity, $k$ the dielectric constant of the material and $r$ the distance ...


1

The permittivity of free space was named when people still accepted the aether. One might think it ludicrously named since we keep the name when we have removed the concept by which it was named. I had grown used to the convention that in natural units $\epsilon_0 = 1$, meaning that it is just a conversion constant for units of charge to conventional units ...


2

Why is $ϵ_0$ in Coulomb’s law permittivity of free space if since the free space has nothing (unlike the old concept of ether)? It's the consequence of how we've defined our unit of charge, the coulomb. In other systems of units the numeric value of $\varepsilon_0$ may be different. In particular, in Gaussian system it could be taken as $\varepsilon_0=\...


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Electrostatics (and magnetostatics) remain valid without modification for low velocities, which means $v/c \ll 1$. When this is not the case one must use (special) relativity and account for the transformations of the electric and magnetic fields under Lorentz transformations.


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The statement that Coulomb's Law is only for static charges is concerned with accuracy, but does not imply that the force no longer acts. A disturbance in an electric field moves outward at a finite speed (c), so the force on a second charge may not reflect that the first charge has moved. Or, if the second charge is moving, it may experience an ...


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Your first reference defines the symbols and makes it clear that the formula refers to the twisting of a wire. Since no lever arm is given, the F must symbolize a torque.


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In these calculations one is interested in the magnitude of the interaction, which is predicted correctly by applying Coloumb. For rigorous treatment of intermolecular and atomic interactions one must resort to quantum theory anyways.


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In school, we simplify slightly. We talk about science as if it tells us the truth about the universe in what philosophers would call an "ontological" sense. In reality, science is all about making models that explain things and predict things. We make our models, then turn up the heat, and see if they hold or if new behaviors occur. Often we find that ...


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The electromagnetic interaction is one of the four fundamental forces of the universe. It just so happens that there are two types of charges that interact under this interaction. If you put two particles with the same type of charge together, they repel each other. Two with different types of charge, they attract each other. Nothing in particular pushed us ...


3

To the first question, yes. Two particles with opposite charges will attract, and if the electromagnetic force was the only force in the universe, AND the particles start off as either stationary or on the exact right trajectory to collide, the two will collide. It should, however, be noted that if the trajectories are even slightly off, the two particles ...


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