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1

Both can happen simultaneously. This happens in binary star systems all the time. Work done on object A as it moves from position 1 to position 2 is calculated by $$\int_{\vec{r}_{1A}}^{\vec{r}_{2A}} \vec{F}_{total\,on\,A}\cdot\,d\vec{r}$$. That changes the kinetic energy of A. It could be negative which means the kinetic energy decreases. Some might say ...


0

Draw a very good sketch for yourself. Then integrate d$\vec{E}$ for every point charge in the sheet, for any random (x,y,z) point not in the sheet, but let that (x,y,z) point be constant for the integral. Writing the expression for d$\vec{E}$ is the challenging, and educational, part. Have fun and learn a lot!


0

Fundamentally you just need to know which direction energy flows. If energy flows from object (or system) A to object (system) B, object A is doing work on object B which is the same as saying object B is being worked on by object A.


2

Indeed, the $\vec{E}$ field in a parallel plate is independent of distance from the plate. This works because of the assumption $d \ll$ length of plate (thus, we can ignore side effects of the plate). And as Bort pointed out, it is the Voltage $V$ that scales linearly with respect to distance from the plate, while $\vec{E}$ will remain constant.


0

Both objects are responsible for the field, and the total gravitational (or electrostatic) force field is the linear superposition (sum) of the force fields arising from each object on its own. So, for example, if you have two point masses of mass $m_1$ and $m_2$ at positions $\vec{r}_1$ and $\vec{r}_2$, the field at point with position $\vec{r}$ will be: ...


1

Based on the title of your question, there are only two objects. I'm going to infer that you are analyzing the motion behavior of one of those objects based on the influence of the other. I'm also going to assume that the influence is gravitational and not electrical. That's the context of your question. You will only show the gravitational force vector ...


3

Yes, this is correct. Also there are field lines going out from the top of the top plate and the bottom of the bottom plate. And far away, the field lines should look like those of a single point charge, with charge equal to the total charge on the two plates.


1

Gravitational field vectors conventionally are represented pointing toward the gravitating body whose gravitational field is being analyzed. If two gravitating bodies are mutually attracted to each other, and one is in orbit around the other, the center of mass of their system is called the barycenter, and both orbit around the barycenter. This results in ...


0

Well, insulators can store charge. It is just very difficult to get a noticeable amount of charge into an insulator, since they do not conduct electricity very well..


0

If the sphere has a volume charge, it implies the sphere is a non conductor, in that case E field exists within the sphere(there being no scope for electrons to move under the effect of these field lines as it is a "non-conductor"). When you construct a cavity within this volume.. By gauss law, you get the closed Integeral of E wrt area to be 0 within this ...


1

The electrons do not even enter the wire, because the redox reaction between the substances in each of the nodes never occurs. Once the wire is connected to each of the nodes, electricity will flow through as electrons will be more attracted to the node with the greater reduction potential.


0

What is the cause of the Lorentz Force? The "screw" nature of electromagnetism. Minkowski referred to it in Space and Time, as did Maxwell in On Physical Lines of Force: "a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw". This is why the right hand rule ...


1

Apart from philosophical debates: What is the cause of any force? A gradient in the energy. I'm not in the mood to do any actual calculation, but the energy density of a magnetic field is $\sim \vec{H} \cdot \vec B \sim B^2$ (here at least). Now, we are looking at a field that is created by superposition $\vec B = \vec B_1 + \vec B_2$ with $\vec{B}_i$ being ...


-1

Yes, it is possible to explain it. The reason are the magnetic dipole moments of electrons and its intrinsic spin. More see my explanations in this paper. Electrons have magnetic dipole moment and intrinsic spin. (This spin is really a rotation due to the Einstein-de Haas experiment.) When moving electrons came into a non-parallel to the electrons movement ...


0

In your expression for $E_x$, $q_2$ should be minus. Plus is for positive charge & minus is for negative charge. The direction of electric field from a point charge is taken to be radially away from that charge i.e. positive-ness. The direction of electric field is taken to be radially towards the charge i.e. negative-ness. $cos(45)$ is coming because, ...


5

No, one cannot explain the "cause" any deeper than the explanation that Lorentz force and Maxwell equations are postulated as a description and experimentally are found to foretell correct results. One can give certain motivations why these might be the correct equations: for example, the Lorentz force law is one of the simplest Lorenz covariant laws one can ...


0

The right way to derive the total energy is to put the particles one by one. In a space centered at $e_1$ and having nothing else, the energy to bring $p_1$ from far away to a distance $r_0$ is $E_{e_1,p_1}$, this you know how to calculate. The energy to put $e_2$ at its position will have two terms coming from $e_1$ and $p_1$. By superposition, this ...


0

If the shell is perfectly spherically symmetric, and the charge is perfectly evenly distributed on it, then the total field due to every singel charge is zero at every single point inside the sphere. This also happens with gravity, there is no gravitational force inside a uniformly distributed shell of mass due to the shell of mass. While each piece of ...


2

The statement means that the net electric field at any given point inside the sphere adds up to zero due to all the varying contributions by the charges on the surface. They exactly cancel out, and hence for any point inside the sphere, the value of electric field is exactly zero.


0

This question is answered in the Wikipedia article on the shell theorem. The gist is that it is not the total. But going beyond that, I think your question actually reflects a misunderstanding of what "electric field" means. The electric field is something which has a value at every point in space. If you try to calculate a total, e.g. by integrating the ...


0

The NCERT formula is correct if used with vector notation as the direction of electric dipole moment is from -q(negative charge) to +q(positive charge) and the resultant electric field at any point on equatorial line is in direction opposite to the electric dipole moment so negative sign is used. The other formula which does not include negative sign is ...



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