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Questions tagged [charge]

A fundamental property of matter which causes it to experience electromagnetic forces.

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“Derivation” of continuity equation

The surface integral of j over a surface S, followed by an integral over the time duration t1 to t2, gives the total amount of charge flowing through the surface in that time (t2 − t1): $${\...
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Why do we still call the electron charge the elementary (EM) charge?

The electron is an elementary particle, part of the SM, pointlike, with no substructure, or spatial extent. Its intrinsic properties include its EM charge, which we still call the elementary charge. ...
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Potential of hydrogen atom solution of the Laplacian: Missing boundary condition to fix integration constant $c_1$

I have following problem, I want to calculate the classical potential $\phi(r)$ of the hydrogen atom in its ground state. The charge density is known: $$\rho(r)=\frac{-e_{0}}{\pi a^3}e^{-\frac{...
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Why are there 6 interactions with 4 positive charges?

From a homework assignment, there are 4 spheres spaced 1cm apart. Each of the spheres are charged to +10nC and weigh 1 gram. The question wants us to find the final speed of the charges once they've ...
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If the cross-sectional area of a wire doubles shouldn't the current also double?

In this question the answer is B but I don't understand how that could be possible considering the area has doubled.
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When to use $e^{-t/RC}$ - Capacitor discharge and charge

Respected Team Members, I am learning how to calculate the amount of time it takes to charge/discharge a capacitor. The Formula given in the text book is $$\ V_{f}=V_{s}(1-e^{-t/RC})$$ But we ...
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1answer
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Gauss' Law not including all of the system

Suppose we have a system of two parallel conducting plates charges $Q$ and $-Q$ and charge densities $\sigma$ and $-\sigma$. In this case, to find the electric field, Gauss' Law is used with a ...
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2answers
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Proof of continuity of voltage across a capacitor

It is known that the voltage drop across a capacitor is a continuous function of time. This means that, for each instant t0, we may write: V(t0-) = V(t0+) This relationship is very used in the time ...
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What is the function $q$ in the definition of charge density?

Supposed we define $\lambda = \frac{dq}{dl}$. If I think of this intuitively, this makes sense; the linear charge density at a point is tiny amount of charge at that point divided by the tiny length ...
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1answer
26 views

Electrostatics, measurement of charge

How did physicists come up with a standard for measuring charge? How an electrical measurement of charge was made?
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29 views

Energy of the system of similar charges

We know that two same charges repel each other. To stop the charges from going away we have to exert an external force and hence energy is used. But if in a vacuum two similar charges are placed near ...
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4answers
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The potential at a point

According to my book, 'The potential at a point is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point.' But I wonder how it is possible. As the ...
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The energy stored in capacitors in series [on hold]

If there is a capacitor of $2$ micro farad and $0.5$ micro farad in series and the charge on the combination of the two capacitors is $0.8\times 10^{-6}$ C. How would you find the energy stored on ...
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Conservation of Charge vs. Conservation of Energy

Is conservation of charge ever violated like conservation of energy is violated during cosmological expansion? I am trying to understand this with respect to Noether's Theorem.
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If voltage represents an energy difference between two points, why don't electronic appliances all use the same amount of energy?

As I understand it, voltage is an energy difference between two points. $$V_f - V_i = - \int \mathbf{E} \cdot d\mathbf{s}$$ But consider a toaster and a refrigerator each using their own 120V ...
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Gauss law in electrostatics

Consider a solid conductor,if the conductor makes a free electron inside that due to thermal energy ,so that causes one positive ion inside the conductor, my question is according to gauss law inside ...
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$E$ outside a Metal Spherric Shell with a off-center Point Charge inside Shell

If a charge +Q is placed inside a metal shell (NOT at the center), as shown below. I can understand that E will be 0 between inner surface and outer surface due to this is a conductor. Then according ...
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1answer
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What's the electric field in a sphere with charge $Q$ and an inverse linear/square law density of charge?

In Classical Electrodynamics by Jackson problem 1.4 asks to find the electric field as a function of the radius of a sphere charged with a charge Q and with a spherically symmetric density that goes ...
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Is the centre of charge always within the centre of mass of an object?

What I am confused about is whether the charge of an object is concentrated within the centre of the mass itself, or does it change depending on the situation?
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3answers
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How do we arrive on the same expression for Gauss's law when deriving it for a sphere or any other figure (say a cylinder)?

For a circular surface, the surface area of the circle is cancelled by factors in the denominator of $E$, leaving behind only $Q/\epsilon_0$. But what about when we conside a cylinder? How so we ...
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1answer
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$CP$-transformation for spinor field. $C$ and $P$ do not commute?

I am bothered by an exercise about CP transformations where I get the result that CP acting on a Dirac spinor field is not the same as the PC transformation. The exercise states the following ...
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How to perform integration for all of space?

Two conducting spheres of radii $a$ and $b$ have charges $Q_1$ and $Q_2$. Distance between their centres is $R$. If ${\vec E_1}$ and ${\vec E_2}$ are electric field vectors due to the two spheres at ...
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Can one assume during the discharge of lightning, some energy is dissipated as heat? (High School Physics)

I was doing homework, and the following appeared as a question: A negatively charged thundercloud above Earth's surface may be modeled by a parallel plate capacitor. The lower plate of the ...
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Boundary conditions for an infinite line charge and grounded conducing plane

I'm not asking for a solution to the problem, I'm confused about what I should set the boundary conditions to, it's obvious that $V=0$ at $z=0$ because of the grounded $xy$ plane, but I don't know ...
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2answers
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Best representation of a proton in non-static spacetimes

The classic way to represent a proton in flat spacetime is to use a simple point charge, $$J = (e \delta(r), 0)$$ But if we're using an arbitrary metric (let's assume still globally hyperbolic ...
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1answer
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Poisson's equation and electric field interpretation

My question is this: Are all solutions to Poisson's equation for a certain charge density such that the negative gradient of them will give me the electric field? In deriving the equation, we say ...
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On the microscopic description of a steady electric current

In Purcell's Electricity and magnetism, page 137, the author derived a formula describing the average velocity $\overline{\textbf{u}} $ of positive ions inside a conductor, a gas made of neutral ...
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1answer
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Does Gauss' law simplify even if charge density is dependent on angle?

We know that with Gauss' law applied to a charged sphere simplifies due to the symmetry of the sphere and we can take $E$ outside of the integral, but what if the charge density $ \rho$ depends on ...
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2answers
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Electric Field Lines between two equal charges end at the midpoint, violate rule that lines only start/end at charge/infinity

At the midpoint of the line joining two equal point charges, the field is zero, and the electric field lines on this line joining the charges each begin at a charge and kind of end at the midpoint. ...
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1answer
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How can charge reside inside a solid sphere of charge?

I was studying the electric field and potential of a solid sphere of charge. In my textbook it is mentioned that we distribute electric charge in the interior of the sphere. I had learnt that in a ...
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2answers
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How to find the electrostatic potential of a hydrogen-like charge density?

I've been trying to find the scalar potential that would correspond to the charge density of a ground state hydrogen atom. The result is known, and the inverse of my problem can be found e.g. in ...
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1answer
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Reconstructing Charge Distribution from Multipole Expansion

Let $\rho$ be a static, discrete or continuous charge distribution, and $\phi(\mathbf{r})$ the corresponding electric potential. We may expand $\phi$ in a multipole series, $$ \phi(\mathbf{r}) = \frac{...
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Conserved charges generate transformations

Focussing on classical mechanics of a point particle, WLOG since it captures the relevant information for field theory and generalises to the quantum case, how do we show -- in general -- that ...
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Do photons influence charged particles? [duplicate]

As a neutrally charged particle, a photon shouldn't interact electrically with another charged particle. However, since photons are electromagnetic waves, they should interact with charged particles, ...
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1answer
80 views

Why is a Coulomb the charge of $6.24 \times 10^{18}$ electrons? [duplicate]

Where does the $6.24 \times 10^{18}$ number come from? How was it historically derived? I know that $1$ C $=$ $1$ A s but that just pushes the question down another step, and another and another, at ...
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Is it correct to say that electro-static potential of a charge is the energy of a motionless charge?

Is it correct to say that electro-static potential of a charge is the energy of a motionless charge? I ask this to better understand this (great) answer;
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1answer
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Can total charge be transferred from a conductor to another isolated conductor?

Suppose a conductor is charged (Total charge $Q$). Is there any method by which we can transfer the whole charge Q from the initial conductor to another uncharged isolated conductor? What another ...
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5answers
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To store 1 Coulomb of charge [closed]

One teacher told me that to store 1Coulomb charge we need a material of about 7 times of Earth. And another teacher told me that what he said was wrong. who is correct?
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1answer
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Differences charge quantity and electric charge

First of all,my english is not well,so sorry for reading. As a senior middle school from China mainland,I am teaching physics about electri field.I with my workmates,get a problem now.We can not get a ...
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1answer
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What is the physics interpretation of work done of zero when moving a charged particle on an equipotential surface?

Assume I have a test charge of + 1 coulomb. If I move the test charge from a point with potential of +9 volt to another point with potential of -1 volt then the work done by me is -10 joule. This ...
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1answer
49 views

Force on a Charge

I apologize, as this question is quite basic. Suppose we have a point mass of mass $m$. Suppose it is at position $r(t)$ at time $t$. Then the magnitude of the force on this mass is $\ddot r(t) m$ ...
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Do charged conductors exhibit an equipotential surface even when subject to an $E$-field?

A charged conductor, in the absence of an electric field, attains an electrostatic equilibrium such that its surface has a constant potential. When a neutral conductor is placed in a uniform electric ...
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Field of a uniformly charged disk: integration question

In my book (University Physics by Young and Freedman), during solving the common example of finding the electric field along the x-axis from a uniformly charged disk, they arrive at this differential ...
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2answers
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Why bending or reorienting the wire does not change the validity of Kirchhoff's junction rule?

Kirchhoff’s junction rule is based on conservation of charge and the outgoing currents add up and are equal to incoming current at a junction. but Bending or reorienting the wire does not change the ...
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1answer
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From volume density to surface density

Let us say we have a volume $V$ having a volumetric mass(charge) density $\rho(x,y,z)$. Suppose we have a smooth surface $S$ within the volume with a surface mass(charge) density $\sigma(x,y,z)$, if ...
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0answers
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Intuitive explanation why electrons move from low to high electric potential

I know almost nothing about physics but am about to learn some electronics. I have trouble understanding why electrons move from low to high electric potential based on the definition given on the ...
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1answer
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Charged conductor in an external electric field

If we put a conductor in a place where there is a uniform electric field, then the field will change. Take for example the case of a conducting cylinder, then the field lines would curve to return ...
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2answers
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On proving that charge is linearly proportional to potential for a conductor

In Mr. Purcell's Electricity and Magnetism, page 103, it is stated, An isolated conductor carrying a charge $Q$ has a certain potential $\phi _{0}$, with zero potential at infinity. $Q$ is ...
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1answer
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What happens to the charge density under parity?

A question came to me when I tried to think about the parity prperties of the Maxwell's equations. The charge density $\rho(\vec{r})$ actually stands for a scalar quantity $\rho(x,y,z)$. Since the ...
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2answers
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From Poisson's equation to Laplace's equation [closed]

I want to understand how exactly $$ \nabla^2 V = - \frac{\rho}{\epsilon_0}$$ turns into $$ \nabla^2 V = 0.$$ Of course it is by setting $ \rho$ equal to $0$ but what does setting $ \rho$ equal to $0$ ...