Charge Definition and 1000 Threads

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?

Let us say we have a cavity inside a conductor. We then sprinkle some charge with density ##\rho(x,y,z)## inside this surface. We have two equations for the electric field $$\nabla\times\mathbf{E}=0$$ $$\nabla\cdot\mathbf{E}=\frac{\rho}{\epsilon_0}$$ We also have the boundary conditions...

I couldn't solve the question. Can you help me?

I've been discussing Newton's Shell Theorem re: gravity with someone, and thought of the analogy to charge. 1. I think the net effect on a negative charge inside a hollow sphere of positive charge will be zero. i.e. No net attraction. Yes? 2. But what would happen to the magnetic field if the...

The problem is symmetric around the z axis, thus the force must be in the z direction only. I tried dividing both rings into differential elements, then integrating through the upper ring to get the z component of the total force on the upper ring due to a differential element of the lower ring...

I quite understand the fact the EPE (Electrical Potential Energy) of a system of two charges are U = k*qQ/r, Q is fix. however when it comes to three charges i get lost. because my reasoning is : if q1 is fix then the EPE of the system when q2 is brought is U2 = k*q1*q2/r12, when q3 is brought...

Electric potential energy at initial: Ee=kq1q2/r =(9 ×10 ^9×1.5×10^-6×(-5)×10^-6)/0.1 =-0.675J Electric potential energy at the closer point: Ee=kq1q2/r =(9 ×10^9×1.5×10^-6×(-5)×10^-6)/0.05 =-1.35J Δv=ΔEe/q =(-1.35+0.675)/1.5×10^-6 =4.5×10^5V or: Initial position...

Modern batteries use double-sided anode and cathodes for greater energy density. Series wiring of batteries is typically accomplished by connecting the anode of one cell to the cathode of another. However, can series be accomplished by stacking double-sided anode and cathode alternatingly with...

All the references I find refer to safely charging lithium cells by a method like this: https://www.powerstream.com/li.htm The next page shows the effects on capacity of charging to less than the 4.2 V terminal cell voltage. For example, charging to 4.0 V still provides 73% of the capacity...

Hope someone can help!

All are used to finding the image charge induced by a source charge outside a conducting sphere. The solution is supposed to also work for the case where the source charge is inside the conducting sphere, in which case the sphere is now a conducting cavity. But the solution suggests the image...

hello Witch of these are certain sentences? a-\dfrac{e}{m_e}>\dfrac{H^{-}}{m_{H^{-}}}\cdot{1000} b-\dfrac{e}{m_e}>\dfrac{H^{+}}{m_{H^{+}}}\cdot{1000} The first accurate measurement of e/m was made by english physicist J.J. Thomson in 1897, who demostrated that the quotient charge-mass of the...