Charged Definition and 1000 Threads

This is the initial setup of the problem: The electric field due to the ring is: $$E = \int\frac{k(dq)}{(\sqrt{R^2 + x^2})^2}\frac{x}{\sqrt{R^2 + x^2}} = \frac{kqx}{(R^2 + x^2)^{3/2}}$$ the force on the rod due to this Electric field produced by the ring is: Consider a differential element...

Question My attempt for the 1st part, when r = 1.5 m Could someone confirm my answer?

To find the initial potential energy of the system we can assume the disc to be placed inside a hollow sphere of the same radius and ##\sigma##, the potential energy inside a charged hollow shell is: $$V = \frac{\sigma(4\pi R^2)}{4\pi \epsilon_0 R} = \frac{\sigma R}{\epsilon_0}$$ the potential...

Using Gauss's Law By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane. We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox". The charge enclosed is...

(Apologies for a basic question) Do charged particles always have spin ? Maybe a better question is, are charge and spin always associated ?

Hello there, I'm perplexed as to why the capacitor is DC-blocking, but the battery (DC) may charge the capacitor. I'd never considered it until I recently read it in a book. I honestly have no idea what's going on. If anyone has any idea why this happens, please let me know. I've read some...

I am interested in particular in the second integral, in the ##\hat{r}## direction. Here is my depiction of the problem: As far as I can tell, due to the symmetry of the problem, this integral should be zero. $$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$ I don't believe I need to...

The strategy will be to figure out what ##dq##, ##\hat{r}_{dq,p}##, and ##r_{dq,p}## are, plug them into the expression for ##d\vec{E}_{p_r}##, then integrate over ##d\vec{E}_{p_r}## to obtain ##\vec{E}_{p_r}##, the electric field at ##P## due to the arc on the right. Then I will repeat the...

I attempt to solve the problem in the picture below.

Let's say you have two extremal black holes containing the maximum amount of possible charge. Now let's say they're orbiting each other such that they will eventually merge. As the black holes merge they are producing gravitational waves. Once the merger is complete the new black hole mass will...

If a charged particle moves through a potential difference, it gains kinetic energy but does it also lose potential energy? When I accelerate a particle and then I "free it", what happen to its potential energy if the total energy should be conserved?

Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...

The question is very simple: Is the flow of charge, or current, related to a closed path or there will be a potential difference without closed path to allowing the flow? I mean, If I have a battery that maintain 5V of potential difference through its terminal, I believe there is an amount of...

I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...

I am having trouble understand where area circled in red. I get that lamda is Q/L. The charge is +Q. Length is pi/R/2. I am having trouble understanding why the length is pi/R/2? Is it because the circumference of a circle is 2*pi*R and since we have broken this problem down to just...

Hi , I've been trying to manage a solution in my head and i think I'm on the right path , i just need some approval and maybe some tips. So it's obvious I can't solve this without integration because law's only apply to point charges , and i can't shrink this object to a point as i could do with...

In a previous thread* the field in a charged ring was discussed and it was shown to be not zero except at the center. In *post #45 a video is referenced that says the field diverges as one gets close to the ring and it was argued that at very close distances the field looks like an infinite line...

General relativity tells us that an object in free-fall is actually inertial, following a geodesic through curved spacetime, and not accelerating. Instead, it's objects like us, on the surface of a large body, that are accelerating upwards. Maxwell's equations also tell us that accelerated...

I have broken the ring into a top arc and a bottom arc. First, let's assume an imaginary charge of +1 C is placed at point P. We will determine the force on this unit charge from top and bottom arcs. The charges in the top arc will result in electric fields that will all cancel each other...

When I look at the relevant equations, then there is no mention of field for a point on the surface of the shell, so it gets confusing. On the other hand, I feel the radial E will get stronger as we approach the surface of shell and magnitude of E will approach infinity.

When I read things about magnetism on internet, I don't understand at all about one thing: If a moving particle receive a force if it's in a magnetic field, so it should accelerate, so what happen if we change the referential so that the particle now don't move? The particle shouldn't receive...

1. For regions that contain charge density, does the 1st uniqueness theorem still apply? 2. For regions that contain charge density, does the 'no local extrema' implication of Laplace's equation still apply? I think not, since the relevant equation now is Poisson's equation. Furthermore...

Hello, I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...

(A) incorrect, because opposite signs attract, and the sphere would've been drawn to the charged rod. (B) correct, according to the answer key, but if the charge of the sphere and the charge of the rod are the same, then wouldn't they repel each other? I'm confused as to why this is the correct...

Suppose we have a charged metal tube through which charged ions of compressible fluid is passing. I want to know whether the boundary layer will still form that will resist the flow or the flow will be smoother. We all know how strong electromagnetic force is and this will push the ions away...

I looked at the solution of this problem since its a solved problem. I am having doubts with the charges relationship as is mentioned in screenshot below. The charges ##{q_3}^{'}## and ##{q_4}^{'}## are the charges after a a state of balance is reached. Why would the charges have the...

consider a small element that subtends an angle ##2\Delta \theta## at the center of the ring. balancing the forces on this element gives: (let the field due to the ring be at its circumference be ##E##). $$2T\Delta \theta = E(dq) = E (\frac{Q}{2\pi})(2\Delta \theta)$$ $$T = \frac{EQ}{2\pi}$$ now...

The task is to find the magnetic field between the 2 long cylinders, which extend to infinity. Integration is involved to find the total current passing through the Amperian Loop shown below. What I do not understand is why only sides 1 and 3 contribute to that B ds part of Ampere's Law. Isn't...

I thought the equation listed should be used, with the 'charge density' determined by the point charge multiplied by the area of the plate, but not sure if that makes sense.

I thought it might be the case that the "2m away" wasn't applicable as the electric field doesn't change if the point away is less than the length of the plate, so I thought I should use the equation listed. All examples I can find talk about two charged plates, or the effect on cylinders...

Will translation parallel to x-axis work ? Else please suggest the symmetry? And does symmetry here refer to the symmetry of the sheet which causes the symmetry of the field or something else? Please be kind to help.

I find a exercise in Leonard Susskind's book Classical Mechanics the Hamiltonian of a charged particle in a magnetic field(ignore the electric field) is $$H=\sum_{i} \left\{ \frac{1}{2m} \left[ p_{i}-\frac{e}{c}A_{i}(x) \right]\left[ p_{i}-\frac{e}{c}A_{i}(x) \right]...

Please help me on this question I have tried to do it many times but I end up getting the wrong answers. I have show my work what I have done.

So here was my first go around at it: At first it made sense in my head but don't think my process is correct. Then i noticed the example in the book: I guess the reasoning isn't 100% there in my head and if i don't have an actual σ, how will i cancel out any legendre polynomials due to...

Maybe this will help.

I am just a bit confused here. Would doing this even change the electric field direction at the center at all? I'm thinking no, but a bit of direction would be appreciated. This problem is really simple, I'm just a bit confused.

The physics behind this problem is that an electric field is induced (by Faraday's Law), when the B field is switched on. Charges on the ring now experience a force as given by dF = E dq. Apparently, because of this, the ring starts rotating. I understand that charges in an insulating material...

I thought up of this problem myself, so I do not have solutions. I would appreciate if you could correct my approach to solving this problem. Firstly, the charge induced on the inner surface of shell B is -q, and so the charge on the outer surface of shell B is Q+q. The energy stored can be...

The force per unit area (Pressure) on a part of the sphere is given by F = (E outside + E inside)/2 * Q = 0.5 (kQ/R^2) * (Q/ 4piR^2) = (Q^2/ 32pi^2 e0 R^4). I understand the above line. The solution then says this pressure is exerted on the contact area between the 2 spheres, as given by...

I traced a spherical X-ray Gaussian (green) where the negative charges were diametrically opposite. My question is this: I can transform the entire charge of the Gaussian sphere into a point charge placed in the center. So, can I analyze only the electrical forces of the two negative charges...

Hello! This is probably something simple but I am getting confused about it. Assume we have an electric field along the z axis given by ##E = -kz##, with ##k>0##, so the field on both sides of the xy-plane points towards the origin. Let's say that we have a positively charged ion at the origin...

Charge QQ is uniformly distributed along a thin, flexible rod of length LL. The rod is then bent into the semicircle shown in the figure (Figure 1).Find an expression for the electric field E⃗ E→ at the center of the semicircle. Hint: A small piece of arc length ΔsΔs spans a small angle...

I am not able to intuitively understand the reasoning behind why the presence of dielectric between oppositely charged plates, let's say, reduces the force of attraction between the plates. I understand to some extent that electric field lines prefer to flow through dielectric (or insulator)...

2 separate big conductors initially charged Q1 and Q2. Then connect them with an ideal wire (no resistence). The charges Q1 and Q2 will go to the 4 surfaces (marked red). All the 4 surfaces have an area A. Suppose the 2 conductors form an ideal parallel plate capacitor. How to determine the...

2 separate big conductors initially charged Q1 and Q2. Then connect them in a circuit with a battery of emf V. The charges Q1 and Q2 will go to the 4 surfaces (marked red). All the 4 surfaces have an area A. Suppose the 2 conductors form an ideal parallel plate capacitor and the wires in the...

Admittedly I found similar threads here already but due to my rather lacking math skills I wanted to go through this myself. As for the math side, I see various different equations with which this is treated can someone please provide the formulas for calculating B field from a rotating charged...

Griffith's says this, and I'm not exactly sure why... If you had a solid, spherical, and externally induced conductor... Does this mean that IMMEDIATELY outside, when you're infinitesimally close to the surface, E looks like this? If you surround the entire conductor with a Gaussian surface...

"If the sizes of charged bodies are very small as compared to the distances between them, we treat them as point charges". Can you explain me the statement. And what does "sizes of charged bodies" refer here. Thanks