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13

There is a sort of analog called gravitomagnetism (or gravitoelectromagnetism), but it is not discussed that often because it applies only in a special case. It is an approximation of general relativity (i.e. the Einstein Field Equations) in the case where: The weak field limit applies. The correct reference frame is chosen (it's not entirely clear to me ...


4

There is a gravitational analogue of the magnetic field. See gravitoelectromagnetism and frame dragging on Wikipedia.


2

I solved my problem numerically, using the diffusion equation $\frac{\partial V}{\partial t} = -k\nabla^2 V$, with the following boundary conditions: Voltage at point D is fixed at 1.0 Voltage along the vertical line halfway between points A and D is fixed at 0.5 (voltage at point A is 0.0, use symmetry so we don't have to simulate the left half of the ...


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We take positive charge as a test charge because positive charge is higher potential and negative charge is lower potential. Therefore, influence of positive charge on other charges is greater than negative charges. We can also take negative charge but the effect will be lower.


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You're so close to the answer I'm not sure how to nudge you along without basically just giving you the answer. I'll try anyways. There are some troubling conceptual mistakes you've made in an otherwise straightforward derivation. For starters : The reason I don't set $E_0 x_0$ to zero is because there is no $1/x$ term; otherwise I'd be able to make the ...


2

One: I honestly don't know. I was already hard for me to find this experiment in german - although german is my mother tongue. ^^ I finally succeeded with Ringentladung, which I tried to translate into english but the only thing I could find is this. Maybe a native speaker can help here? Two: The electric discharge - which causes the gas in ...


0

Ion lenses (either of the electrostatic or magnetic variety) typically all have something in common: the fields are such that particles which are off-axis are more strongly bent towards the axis, and particles that are on-axis remain unaffected. Using electrostatics, this is most easily achieved using an Einzel lens. This is a lens that consists of two or ...


3

There aren't E and B fields in the entire universe. For example, there are no electric fields inside a conductor. I'm sure there are quite a few other such examples. If you mean "why are there electromagnetic waves throughout the entire universe?", one answer is because the radiation field drops like $1/r$, so the field from a single source never ...


0

This is an example of Faraday's Law, one of Maxwell's equations: $$ \nabla \times E = - \frac{\partial B}{\partial t} $$ Which relates the curl of an electric field to the time-derivative of a magnetic field. If you consider a static electric field, you can describe the entire system with only Gauss's Law: $$ \nabla \cdot E = \frac{\rho}{\epsilon_0} $$ ...


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This is an extremely common mistake in introductory EM - from students who actually spend time thinking about the problem, anyway ;-) Use Gauss's law in both cases: In the case of infinite plates, you do not have the result you give first. A Gaussian cylinder has two disks on either side of the plate, so $$E_1(2A)=\frac{\sigma A}{\epsilon_0}\rightarrow ...


1

Counterexample: An electromagnetic plane wave in free space (no charge or current) at a fixed frequency and linear polarization has oscillating electric field in one (unsigned) direction normal to direction of propagation. These field lines are not closed. Note: Although Maxwell's equation is "Faraday's equation plus other stuff", adding more equation ...


0

Two magnets can be considered as current loops as shown in the picture. Consider magnetic field due to lower magnet and current in the upper magnet. The magnetic field has a radial component in outward direction passing through upper loop. The current in upper loop is anti-clockwise from above which gives the force in downward direction. You can see the same ...


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I will use my limited knowledge to answer your question. As I know, in magnetic objects there are many magnetic dipoles, which in turn is a loop current. So, basically, the magnetic field created by the first object will act a force (Lorentz force) on loop currents of the second object. It's similar to the force 2 parallel currents act on each other. ...


1

I agree with the result, but I would like explain another more general and rapid approach. Because of the radius of the hole is negligible with respect to the radius of the sphere, and the only posible direction for E compatible with the symmetry is the z axis, and finally having in mind that the tangencial components of E are continuous, the solution is ...



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