Charge Definition and 1000 Threads

For the flat spacetime we could just use that partial derivatives commute as well as the antisymmetry of ##F^{ab}##, i.e. ##\partial_b \partial_a F^{ab} = -\partial_b \partial_a F^{ba} = -\partial_a \partial_b F^{ba} = -\partial_b \partial_a F^{ab} \implies \partial_b \partial_a F^{ab} = - 4\pi...

A spherical volume charge (R<=1cm) with uniform density ρv0 is surrounded by a spherical surface charge ( R=2cm) with charge density 4 C/m2. If the electric field intensity at R=4cm is 5/Є0 ,deterime ρv0

Hello PF. I'm just curious. I found the following description in a textbook I am reading. What I'm interested in here is what would $E$ and $B$ look like if the charge was oscillating at close to the speed of light ( means relativistic velocities) ? Thank you.

A metal rod held in hand and rubbed with wool will not show any sign of of being charged. However, if a metal rod with a wooden or plastic handle is rubbed without touching its metal part, it shows signs of charging. Why??

There is a section in the BJT explanation the charge density and the corresponding electric field graphs. But i was not sure how the electric field is derived and hence i started deriving it. Please correct me if my understanding is wrong in posting the question It is an ##npn## BJT. My...

According to my professor, the solution in this book (pages 20-21) for item (ii) is wrong: https://www.u-cursos.cl/usuario/75468645ed16a71af6da3ffd813d47f5/mi_blog/r/Problems_and_Solutions_on_Electromagnetism.pdf

In a conductor, excess charge resides on the surface. That seems odd, because one would think that the overall energy of the system could be lowered by allowing some of the excess charge to move inward and away from all the charge on the surface, but obviously that can't be true, because charge...

When the mass starts sliding down, it will induce a current due to the cutting of B field. By fleming right-hand rule, the B field points into the field, charge going in the direction down the ramp (current pointing down the ramp?), therefore the force should be in the same direction of normal...

Homework Statement:: Hi, It's been a while since I have reviewed my basic semiconductor physics and I have some doubts. In a P-Type doped semidoncutor material, I understand that Group III elements such as Boron are added to a Group IV element such as Silicon and thus the Boron atom has one...

a) Static charge distribution should result in a static electric field? Legitimacy should be checked with curl of E = 0? b) Using the second equation should give is the answer?

In this explanation we need to involve the Dirac delta functions(maybe) but I clearly have a difficulty in understanding it can some one explain me the whole concept of constant or non constant volume charge density.

So, the only thing which came to my mind in order to solve this problem was actually to write down the equations using the discharge function, being given two instants and their corresponding charges... but doing so I'm unable to find anything. Ideally, I'd say I should find the time constant...

Assume that a certain charge distribution ##\rho## generates an electrical field ##E_{ext}## in the surrounding space. We also note the corresponding generated potential ##V_{ext}##. Assume furthermore that a conductor A, with a definite shape and volume, is placed in field ##E_{ext}##, and is...

Could somebody check my solution? I want to know is it correct.

The answer is that the charge density would be -σ, I cannot for the life of me understand why would that be the case. Of course it makes sense but I can't convince myself that it would be the only possible answer. I have tried to apply Gauss law a few times, but it doesn't yield anything.

I first calculated the charge each capacitor has after its directly charged by the 36 V battery. ##Q_1 = C_1 * V = (2 \mu F) * 36 V = 72 \mu C## ##Q_2 = C_2 * V = (5 \mu F) * 36 V = 180 \mu C## ##Q_3 = C_3 * V = (7 \mu F) * 36 V = 252 \mu C## Then these capacitors connect in series, so I...

Electric field for the semi-circle $$E = - \frac {πKλ} {2R} $$ In this case E is equals to 10 N/C Electric field for the straighten wire $$E = 2Kλ * ( 1 - \frac {2y} {\sqrt{4y^2 + L^2}})$$ In this case E is equals to 8 N/C What I'm searching is R, λ, and the length of the wire, so I think...

I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?

Hello everyone, I am new to this site so I hope this is the right place to ask this. I understand simulating electric field intensity using electrostatics because E=V/d makes sense to me. I do not understand how to consider e-field intensity using charge distribution. When is charge...

what I've done so far? -i've determined the vector between the point (4, 0, 0) and the point P. (4, 6, 8) - (4, 0, 0) (0, 6, 8) -The norm of this vector is the radial distance of the line to point P (the value of “ρ” in the formula) √(0^2 + 6^2 + 8^2) = 10 -> ρ = 10 -and its unit vector is...

F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so...

At first I take the uniformly distributed charge and then divide it by the area of the carpet to get the surface charge density σ -10E-6 C / 8m^2 = σ = -1.25E-6C/m^2 Then I divide the surface charge density by 2e0 to get the electric field strength caused by the infinite plane...

Could anyone explain how did Jackson obtain the Taylor distribution of charge distribution at the end of section 1.7 (version 3)?

I have a neutral charged atom. When I bring an electron to this atom what the force will hold this electron with neutral atom?

Quote 1: "[He] accumulated an estimated 30,000 volts of static charge simply by walking around his home town in inadvisably large quantities of non-natural tailoring." Quote 2: "A man left a trail of scorched carpet and melted plastic after static on his clothes built up to a 40,000 volt...

Recently I've been researching parallel plate capacitors and was wondering what effects the material had on the charge capacity of the plate. I found one source for measuring the capacity based on its material, but haven't seen any textbook evidence to support it yet. Any feedback on the...

I'm not sure I understand why I need to use ##d##.. Maybe they want me to have the potential be zero at ##A##? In any case, I have found$$V(B)=\alpha k\int_0^L\frac{x}{\sqrt{b^2+\left(x-\frac{L}{2}\right)^2}}dx+C=\frac{\alpha...

Everywhere I look online I see the formula for the magnetic field of a uniformly moving charge is, $$\frac{\mu_0 q \vec v \times \vec r}{4\pi r^3}$$ but when I calculate it by transforming the electrostatic field (taking the motion along x) I get, $$\frac{\gamma \mu_0 q \vec v \times \vec...

Attached is the subsection of the book I am referring to. The previous section states that the electric field magnitude at any point set up by a charged nonconducting infinite sheet (with uniform charge distribution) is ##E = \frac{\sigma}{2\epsilon_0}##. Then we move onto the attached...

The electric field caused by the surface distribution on a point ##a## meters far from it is$$E(a)=\frac{kQ}{(R+a)^2}$$from which I get$$Q=\frac{(R+a)^2E(a)}{k}=\frac{(R)^2E(0)}{k}=\frac{(0.705)^2\times867}{8.99\times10^9}\approx4.79\times10^{-8}$$and I take its negative because the direction of...

This is the diagram I drew for my calculations: I wanted to see if my work for part (a) makes sense. If there is a variable ##l## that runs along the slant of total length ##L##, a ring around the cone can have an infinitesimal thickness ##dl##. By Coulomb's law, $$\vec{F}=\frac{1}{4\pi...

I understand that this difference is valid for E = 0 and E2 = σ / Ɛ0, but Purcell covers a more general case, and I don't see how this difference is fulfilled in other cases. I appreciate the help you can give me.

This is an example of Griffith's book on bound charge, and the following is the solution to this example. We choose the z-axis to conincide with the direction of polarization. By $$\sigma_b \equiv \mathbf P \cdot \hat {\mathbf n} $$ and $$\rho_b \equiv - \nabla \cdot \mathbf P$$ we can...

Maybe I should use this?

Hello Friends, Please help me to setup 5 [18650] Li-Ion battery of 11.1 volt I describe everything in image. Please check attach file Thanks in Advance

Here is what the solution says: As usual, quote the general potential formula: $$V(r,\theta)=\sum_{l=0}^{\infty}(A_lr^l+\frac{B_l}{r^{l+1}})P_l(cos\theta)$$ The potential outside the sphere is: $$V(r,{\theta})=\sum_{l=0}^{\infty}\frac{B_l}{r^{l+1}}P_l(cos\theta)$$, which makes sense to me...

I sort of understand the meaning of this integral, but I don't know how to evaluate it. I have never evaluated a volume integral. It would be very helpful if someone could explain in other words what this integral means and give an example evaluating it. This is from Purcell's Electricity and...

From Maxwell's equations \partial_\nu F^{\mu\nu}=J^{\mu}, one can derive charge conservation. The derivation is 0\equiv \partial_\mu \partial_\nu F^{\mu\nu}= \partial_\mu J^{\mu} { \Rightarrow}\partial_\mu J^{\mu}=0. However, a circular reasoning exists in it. For the sake of better...

Really don't know if this is wright. Here it goes. Thanks in advance: ##\vec{E}=K\cdot{q}\cdot{\sqrt{\dfrac{1}{r_1^4}+\dfrac{1}{r_2^4}}}\cdot{\left(\dfrac{r_1}{\sqrt{r_1^2+r_2^2}}\hat{i}+\dfrac{r_2}{\sqrt{r_1^2+r_2^2}}\hat{j}\right)}##...

The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by $$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$ Faraday's law of induction for the induced EMF ##V_c## in a coil...

I'm trying to better understand the physics of how Earth ground works. In circuit analysis and other electronic courses they usually present a conceptual picture like below where the Earth is viewed as a path that completes a circuit? In this conceptual view, the current travels on the...

I don't understand why moving charge doesn't affect the magnitude of induced charge. Could someone explain why it is possible? Thanks in advance.

Let us connect a battery of potential difference V to a wire. There is no resistance. Nothing! Now the battery creates some potential difference and the charges in the conducting wire move due to the Electric field created in the conductor by the battery. So, as the charge moves, its potential...

Let point charge q be at y=r. Let there be an infinite conducting plane along the x-axis and z-axis that is neutrally charged. In this case, the method of mirror charges can be used. The plane is replaced by a point charge -q at y=-r. The electric field for y > 0 is the same in both cases...

So this is a question from my lab report on capacitance. The aim of the experiment is to find out the relationship between surface charge density and radial distance from the centre of the plate capacitor. And in this experiment I have recorded 5 sets of data, namely r=0, V=4, r=1, V=3.5, r=2...

The charges are q1,q2 & q. P,Q,O1,O2 refer to positions only. This is a conducting sphere with cavities containing charges. I'm interested in knowing how the charge should be distributed in the sphere. I know the charges induced on the charges of the sphere should be equal and opposite to the...

-------------------------------------------------------------------------------------------------------------------------------------------------- This was a problem introduced during my classical electrodynamics course. I am not 100% sure, but I think I've solved up to problems (a) and (b) as...

Hello, it's been a while since I've done any proper electrostatics, but I have a problem where I have a bunch of discrete point charges within some volume V bounded by a surface S. I am wondering if it is possible to replace the discrete charge density in my volume V by some continuous surface...

Hi, I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in...

How to visualize charge distributions in COMSOL, like showing + or - charges on a surface or a bulk in postprocessing?