All Questions
Tagged with electric-fields potential-energy
142
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Comparing Electric Potential Energy of two Charges
I do not know what I am missing here and would appreciate a little help in figuring out the flaw in my logic. I have a row of positive charges and a row of negative charges as shown in the image above....
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7
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Is it impossible to construct a Faraday cage that can block a *static* electric field?
I think the answer is yes. My reasoning is this: Imagine for argument's sake, we could have a charged negative source that has its field blocked by a Faraday cage. We can transport a positive charge ...
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vote
1
answer
82
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Electric potential energy, Electric potential and self-energy of a body
The total work done to bring all the charges constituting a body from infinity to the body one by one is called the electrostatic potential energy of the body. And if I divide the expression of ...
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1
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Apparent contradiction while calculating potential inside shell due to off center charge
Consider the following scenerio$-$
A point charge $Q$ is placed at an off center point $B$ in a spherical shell made out of a conducting material. We are required to find the potential at the center.
...
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Energy in electric field of an electron?
I am just trying to get an intuition for the Griffiths equation no. 2.45, where work done to establish a field E is given by
Say we want to solve it for electric field due to an electron (point-charge)...
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1
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96
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Potential energy of an electric dipole without any external field
What is potential energy of an electric dipole without any external field?
If its 0 then why? Wouldn't the charges get attracted thus do work so they must have some potential energy.
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1
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Would it be right to say that “Electric Potential” = the potential energy of an individual unit of charge at a certain point in a electric field?
Any replies from people who actually understand the topic (better than me, to say the least lol) and are able to clarify the topic (unlike my teacher), are highly appreciated and encouraged.
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4
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Electric Potential and Potential Energy
Electric Potential definition is as follows:
Electric potential (also called the electric field potential,
potential drop, the electrostatic potential) is defined as the amount
of work energy needed ...
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0
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60
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Interpretation of Equation of energy stored in continuous charge distribution [duplicate]
In the book "Introduction to Electrodynamics" by David J. Griffiths, $\boldsymbol\S$ 2.4.3$\blacksquare $ The Energy of a Continuous Charge Distribution, I came across this equation for ...
12
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5
answers
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Why do we say that electric potential energy is stored in the electric field?
I have been learning electrostatics and came across capacitors. I don't really get why do we say energy is stored in electric field rather than in the charges upon which we or the battery does work. I ...
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1
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Energy stored in a space with electric field is $\tfrac12 \varepsilon E^2$ per unit volume. Why?
I'm a high school student and my book says that once it has been established that a region containing electric field $E$ has energy $\tfrac12 \varepsilon E^2$ per unit volume, the result can be used ...
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28
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Electric potential significance [duplicate]
What is the physical significance of electric potential? I know that over dx length of an electric field it varies but let us assume the field to be uniform, how exactly does the potential still ...
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1
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1
answer
147
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Confusion pertaining to the electric potential energy
First I'd like to explain why I don't think this question is a duplicate of the many other questions about the electric potential and potential energy. Despite there being many questions and answers ...
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2
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286
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Shouldn't the electric potential energy decrease with separation regardless of whether the charges are positive or negative?
I was revising Electric Fields and it came up that if a positive charge moves in the direction of the electric field (so away from a positive charge), then the electric potential energy will decrease ...
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Energy in electric field calculated in two different ways
The equation for the energy density in a region of space where there is electric field, $\epsilon_0E^2/2$ implies that energy in the electric field can only be positive. Consider, however, the energy ...
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1
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The (electrostatic) force on an extended object
It is well known that, if I have a system of $N$ particles acted upon only by conservative internal and external forces, then I can obtain the force on the $\mathrm{i^{th}}$ particle as
$$\textbf{F}_i ...
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Coulomb force from a variational principle
See the attached discussion from Zangwill's Modern Electrodynamics, and in particular footnote 9. The point of this question is to understand how to recover Coulomb’s force law from an assumed form ...
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Can electric potential energy be nonzero when the electric field is zero?
I read on wikipedia that electric potential energy of a point charge in the presence of n point charges can be calculated from this formula:
$$
U = k_eq \sum_{i=1}^{n} \frac{Q_i}{r_i}
$$
However, ...
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160
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What should the electrostatic energy of a continuous charge density be?
Hope this doesn't come off as too pedantic or overinterpreted. I've been working on revisiting electrostatic and electrodynamic energy from first principles, and I have the following stumbling block. ...
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1
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41
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A question on the work done by the electric field? [closed]
It's a well-known fact that the work done by the electric field is given by
$\int -k\frac{{Q(1)Q(2)}}{r^2} dr = \frac{kQ(1)Q(2)}r$
The work being negative as the force and direction of displacement ...
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1
answer
89
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Energy in electric field of an isolated particle?
I learnt that the energy density of electric field is $\frac{\epsilon_0}2E^2$. However, I'm little confused about how can there be energy associated with an electron in empty space.
How can we have ...
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2
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438
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Distribution of interaction energy in electrostatic systems
If we have two electrostatic systems their interaction energy is given by
$$U=\epsilon_0\int\vec E_1\cdot\vec E_2dV\equiv\int\rho_1\phi_2dV\equiv\int\rho_2\phi_1dV$$ Here the integral is over the ...
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3
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398
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Deriving energy in Dielectrics
Note: I am working in the Lorentz-Heaviside system and all the integrals are over the whole space.
Definitions:
$$\vec E= \vec E_f+\vec E_b$$
$$\phi=\phi_f+\phi_b$$
$$\vec D=\vec E+\vec P$$
$$\rho=\...
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1
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73
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Disagreements in derivations of electrostatics
In the derivation of the potential energy of electrostatic systems we get (I am working in cgs)
$$W=\frac12\int\phi\,dq=\frac12\iiint\phi\rho\,d V \tag{1}$$ But $$\vec\nabla\cdot\vec E=4\pi\rho$$ Thus
...
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4
answers
282
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Consistency of existence of point charges and energy in fields
In Feynman lectures, Volume 2 chapter 8 (https://www.feynmanlectures.caltech.edu/II_08.html#Ch1-audio) at the very end Feynman remarks
We must conclude that the idea of locating the energy in the ...
31
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10
answers
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How is energy "stored in an electric field"?
My physics teacher told me the statement "The energy of a capacitor is stored in its electric field".
Now this confuses me a bit. I understand the energy of a capacitor as a result of the ...
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1
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359
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What does negative electrical energy signify?
When we derive the formula for potential energy caused by the torque of a dipole in uniform electrical field we get $U = -pE \cos \theta$. And my textbook tells me that the when the dipole is kept ...
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1
answer
155
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Does electric current flow from higher potential to lower potential or from higher potential energy to lower potential energy?
Here, $O$ is a field charge with a $+T$ charge. $A$ and $B$ are test charges with $+T_1$ and $+T_2$ charge, and they are fixed in place. Suppose the points at which $A$ and $B$ are situated are $P_1$ ...
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411
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Is energy infinite in an electric field?
Energy is defined as the capacity to do work. Work in turn is defined as force x displacement.
An electric field exerts the field in all directions infinitely (even though the strength of that force ...
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Using Variation of Energy for a Dielectric to define the Electric Field
I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
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2
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100
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Potential energy for uniform sphere doubt
For a sphere of radius $R$, with electric charge distributed in uniform way $\rho=Q/V$, we have
$$U_e=\dfrac{3K_CQ^2}{5R}$$
However, when substituting the charge $Q=\rho V=\rho 4\pi R^3/3$, we get
$$...
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132
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Different result when deriving electric force as $dW/dr$ and $-dU/dr$
Work done by electric field, $W$ is the negative of the change in electric potential energy, $U_r$.
$$W=-\Delta U$$
By considering an infinitesimal change in EPE, we can deduce that electric force, $...
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1
answer
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How to use the equations for electrostatic work?
I was reading Griffith's Introduction to Electrodynamics (3rd ed.) when I stumbled upon two equations. In electrostatics, the work required to move a charge $q$ between two points with different ...
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213
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Electric Potential, Work, Potential Energy, and Electric Field [closed]
I don't quite understand these concepts. What is the relationship of electric potential with work, potential energy, and electric field?
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3
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2k
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Where do electrons flow inside a battery? What happens inside a battery?
Sorry, if this sounds silly, but I have had this doubt from a long time. Please help me, I'll forever be grateful to you.
I'm a student of 10th grade. This is my doubt:
What happens when electrons ...
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3
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170
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Why is the force that does the work, when calculating the electric potential energy, symmetric to the electric force? [closed]
"The electrical potential at a point is the work per unit charge required to move the charge to that point (r) from another point which has been assigned a potential of zero ($r_{0}$)". This ...
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2
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66
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Question about the sign of $\mathbf{E}\cdot d\mathbf{l}$ when computing the Electric Potential [duplicate]
I have a question on the derivation of the electric potential for a single charge located at the origin.
The electric potential is defined as $$V\left(\mathbf{r}\right)=-\int_{\mathcal{O}}^{\mathbf{r}}...
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638
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Textbook question on calculation of potential difference between two points
My textbook has the following question
What is the potential difference between two points that are 50cm and 80cm respectively from a point charge of 2uC?
Unfortunately, the textbook has not taught ...
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1
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143
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What formula is this and what does it signify? (Electric Field and Potential)
I probably skipped the useful part of the lecture, but while we were being taught about electric potential energy, my professor mentioned an equation, which he said we will seldom use, but which is ...
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1
answer
40
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Confusion concerning notion and origin of electrostatic potential
An elementary circulation is mathematically defined by: $dC$=$\overrightarrow{OM}$.$\overrightarrow{X}$.
Now, we aplly this to a ponctual charge: $dC$=$\overrightarrow{OM}$.$\overrightarrow{E}$
And we ...
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Why is the work through the element the same as the potential difference if we define potential difference this way?(lumped elements)
In the Feynman Lectures on Physics part ||, chapter 22-3 he defines potential differnce like this:
The picture is an element in a curicuit, the black lines on top and the bottom are the conductors, ...
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326
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Electric potential and field lines
I have learned that electric field lines goes from higher potential to lower potential. First of all, how does this happen?
And if the above is the case then suppose I have two uniformly positively ...
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2
answers
174
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I really don't understand the sign Work and energy in an electric field
This might be a super simple question to answer but I can't find one that makes sense to me and I feel like I am getting conflicting answers. I have always thought that positive work means that the ...
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2
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Why is the sense of the electric field the one that goes from the highest to the lowest values of an electric potential?
To clarify, what's the reason behind it and why is it not the opposite?
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2
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277
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Does an infinite wire of charge have an infinite potential energy per unit length?
I was doing a physics problem in Purcell's E&M book when I encountered a problem that asked to find the work needed per unit length to assemble an infinite wire charge of radius $a$, by bringing ...
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1
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100
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I am confused on how to think about potential energy stored in capacitors [duplicate]
Energy stored in capacitors is represented by
$$U = \frac{1}{2} QV$$
Now I have heard 2 reasons why there’s a half factor, unlike the general potential energy equation, which is $U = QV$.
Capacitors ...
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5
answers
273
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Where is energy in energy density?
I was learning about energy density and it seemed to be defined as the potential energy per unit volume in an electric field
$\frac{dU}{dV} = \frac{1}{2}\epsilon E^2$
But how can just the electric ...
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1
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187
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How does a transfer of chemical potential energy occur in a circuit?
I am aware that simple DC circuits use a battery which is connected to several elements. In the case that the element is a resistor, I read that the circuit as a whole is an isolated system for energy ...
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435
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Doubt in the interaction energy of the dipole in an electric field
Consider a dipole ($\vec{p}$) in an electric field ($\vec E$) making an angle $\theta$ with the field.
We can see that $V_1-V_2=Ed\cos\theta$
In books, the derivation for the interaction energy of ...
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2
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132
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Is there a symmetry between scalar and vector formulas for electrostatic and gravitational potential, potential energy, field and force?
Formulas for electrostatic potential, potential energy, field and force, bearing the subscript 'E':
Electrostatic potential $V_E=\frac{U_E}{q}$
Electrostatic potential energy $U_E=k\frac{q_1\,q_2}{r}...
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