Please, help me find the mistake in this line of thought, or solve the inevitable question at the end. 🙂   suppose there are two facing plates with different charge $Q_1$ and $Q_2$ these two plates are the only thing in the universe because of the charge imbalance, there is electrical energy in the system now I connect the two plates with an ideal conductor of zero resistance the excess charge in one plate goes to the other plate, without dissipating heat at the end there is no more charge imbalance, no more electric energy in the system where did the energy go?
123028
What exactly would happen in the ideal case where a capacitor were to discharge into a wire with zero resistance?  Like in here:  There is still charge on one plate of the capacitor, which will try to go to the other plate to make $\Delta V = 0$ across the capacitor, so there has to be a current $I$.  But as more charge goes to the other side of the capacitor, the more repulsion these will cause to more coming towards them. So I am assuming current cannot just be constant?  I am starting from $$ I = C \frac{dV}{dt}, $$ but I know neither $V(t)$ nor $I$.
114044
I have come to know the electrostatic potential energy in vacuum is given by $${\frac{1}{2}} \epsilon_0\int d^3x {E^2} $$ and this energy  is due to the mutual electrostatic coulomb potential energy. So only a single point charge in space also contributes to some electrostatic potential energy according to $${\frac{1}{2}} \epsilon_0 \int d^3x {E^2} $$  as due to a single point charge also we have an electric field at every point in space. Now I am not getting it physically, why should there be any Coulomb energy in this case as there is no other charge to provide the electrostatic coulomb potential energy?
99225
I'm having difficulty understanding why a floating capacitor will store less charge than a grounded capacitor. Imagine you have two parallel plates and a low DC voltage source like 5V, with the negative side connected to neutral ground, and that you have two different ways of wiring it: In case 1, you connect one side of the voltage source to each plate to make a normal capacitor. The voltage across the capacitor is given by $Q = C V  $ is given by the geometry of the plates. In case 2, you still connect one plate to +5V, but leave the other plate floating and neutral. According to my understanding, charge should still build up on the positive side of the capacitor because it's at the same potential relative to the other plate as case 1, and it has the same geometry. On the negative plate, negative charge should be locally attracted to the positive plate, leaving behind positives, overall keeping the plate neutral. Practically, I'm pretty sure case 2 is wrong. What I think will happen is a miniscule amount of surface charge will be stored in the positive wire to maintain the electric field, but that charge will be way less than the stored charge of case 1. Can you explain where my understanding is wrong/not deep enough?
70630
Basically, which is the correct formula for thermal energy, and is this the same as kinetic energy? My notes are pretty conflicting on this topic, and I'm getting pretty confused.
122843
So the title's a bit irrelevelant. And I'm having a tough time thinking how to describe my doubt but I'll try my best. Apologies if it is vague, do let me know in the comments.   So I just finished reading the work energy theorem and was moving on to the concept of potential energy (which my book explains poorly, or I'm missing something).   I understand that by the work energy theorem the change in the kinetic energy of a body is the work done by an external force force on the body. ✓Got it, the change in the kinetic energy of a body is equal to the work done by the net force  So I moved on to potential energy, where my book tries to explain stuff by starting off with an example in which we're elevating the book of mass $m$ by doing work $mgh$ on it, where $h$ is the height to which it is raised. My first doubt is, since the force we applied is $mg$ (equal to the gravitational force of attraction in magnitude yet opposite in direction), the resultant force on the book is 0. Since the resultant force is zero, the work done by the resultant force on the book should be 0, and there should be no change in the kinetic energy.   Secondly, the force done by us (the external agnecy), is along the direction of the displacement, the work done is positive and so the change in kinetic energy should be positive (by the work energy theorem?)  What am I messing up? Mixing the two concepts (potential energy and work energy theorem)? Yet after the work we do, potential energy increases, not the kinetic energy? What am I confusing?  Edit   So the given answers helped me understand where I was going wrong (somewhat). The change in the kinetic energy of a particle is equal to the work done on it by the net external force (if the particle is the system)   Now I'm having trouble interpreting the work energy theorem for a system of particles. A book explains it by considering a system of two charges (one positive and one negative; attracting each other). It says:     Because of mutual attraction, the particles are accelerated towards each other and the kinetic energy of the system increases   Firstly, how can we consider something which isn't fixed as our system (the charges move...).   Secondly, there is no net force on the system, so how is the kinetic energy even increasing.   PS: I'm still all confused about potential energy. Before my book starts about potential energy it goes on to talk about the work energy theorem for a system of particles, and that's where I'm confused now.
51952
I have a problem with energy conservation in case of interfering waves.  Imagine two harmonic waves with amplitudes $A$. They both carry energy that is proportional to $A^2$, so the total energy is proportional to $2A^2$. When they interfere, the amplitude raises to $2A$, so energy is now proportional to $4A^2$ and bigger than before.  The equivalent question is what happens to the energy with the superposition of two waves that interfere destructively.  Also, if someone could comment on the statement about this problem in my physics book (Bykow, Butikow, Kondratiew):      The sources of the waves work with increased power during the interference because they feel the wave from the other source.
109897
I had the following question on a quiz recently:     A capacitor consisting of two parallel plates, separated by a distance $d$, is connected to a battery of EMF ε. What happens if the separation is doubled while the battery remains connected?    The correct answer was "The electric charge on the plates is halved." However, we were previously given a question in which a circuit consists of a capacitor of 6 μF and a resistor of 300,000 Ω connected to a battery, and the separation between the plates of the capacitor is quadrupled. However, in this circumstance, the charge on the capacitor immediately after the plates are separated remains the same, and the potential difference across the capacitor increases.   I am confused as to why these questions have different answers to them, despite having an extremely similar setup. My best guess is that the circuit in the second question also has a resistor, but I am not sure, and help would be greatly appreciated.
37648
Why is  due to external charge i.e a charge outside a closed surface equal to 0?  P.S:Moreover I found this statement confusing:-  Electric field appearing in the Gauss' law is the resultant electric field due to all the charges present inside as well as outside but the contribution of outside charges in producing flux is zero. Can someone help me understand it.
65780
I’ve been told that coulomb repulsion pushes excess electrons to the surface of a conductor (i.e. sphere) electrostatic equilibrium, and this symmetry causes the net electric field inside to be zero. However, why can’t excess charges just be evenly distributed throughout the sphere? Would that symmetry not cancel the fields from each charge?  It would be helpful if anyone can provide a diagrammatic answer.
24994
Electricity takes the path of least resistance!   Is this statement correct?    If so, why is it the case?  If there are two paths available, and one, for example, has a resistor, why would the current run through the other path only, and not both?
41277
Here are some depictions of electromagnetic wave, similar to the depictions in other places:      Isn't there an error? It is logical to presume that the electric field should have maximum when magnetic field is at zero and vise versa, so that there is no moment when the both vectors are zero at the same time. Otherwise one comes to a conclusion that the total energy of the system becomes zero, then grows to maximum, then becomes zero again which contradicts the conservation law.
2296
What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be destructed. My guess is that the kinetic energy is transformed into potential energy. Or maybe it depends on the context of the waves where do the energy goes? Can someone elaborate on that or correct me if I'm wrong?
39493
Why is the work done on a charge calculated from infinity to a point? Why not from one particular point to other?
84095
Conceptual question:  Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive.   I'm kind of rusty with my mechanics, does the fact that the work is positive mean that to arrange the configuration you have to do work against the electric field? I.e. supply energy via some external force?  In terms of electrostatics, is there a general way of interpreting the sign of potential energy and work?
86341
I was having a conversation with my father and father-in-law, both of whom are in electric related work, and we came to a point where none of us knew how to proceed.  I was under the impression that electricity travels on the surface while they thought it traveled through the interior.  I said that traveling over the surface would make the fact that they regularly use stranded wire instead of a single large wire to transport electricity make sense.    If anyone could please explain this for some non-physics but electricly incline people, I would be very appreciated.
36568
So I started off with electrostatics and everything seemed nice and mathematical and justified and then "DC circuits" happened!  I just cannot understand the model of electron flow in electrical circuits.  Here are my specific doubts-:  1) If potential difference across a tiny cross section of conducting wire is zero, then why on earth does electron flow across that cross section at all? Never mind potential difference across the whole circuit.   2) Is there a constant electric field across a wire connected to a battery? If yes then how is potential difference across a zero resistance wire constant?   Shouldnt it be increasing?  Doesnt it violate ohms law?  If no,  then why do electrons flow at all?  Please take time to consider these doubts and relieve me of my frustration.  I havs searched through the net for this but every answer seems like beating around the bush.  All of the 4 books I have consulted do not address these facts to my satisfaction.   Frankly I think nobody understands this.
26837
The question at hand is:  "Two capacitors of capacitances $C_1$ and $C_1$ have charge $Q_1$ and $Q_2$. How much energy, $\Delta w$, is dissipated when they are connected in parallel. Show explicitly that $\Delta w$ is non-negative."  I'm confused about what the physical situation is. I took the assumption that these capacitors were somehow pre-charged, and then connected to each other in parallel without a voltage source. However, I don't understand how this would work. If a circuit is composed of only 2 elements, I don't see how they could be in any arrangement but series. Nevertheless, I tried solving it that way:  Two capacitors in parallel have the same voltage drop. Charge will be redistributed to make it the same voltage for both. Let $Q_1'$ and $Q_2'$ be the charges on the capacitors after they are connected. Now, picture the equivalent capacitor  $C_{eq} = C_1 + C_2 =$ $\frac{Q_1' + Q_2'}{V_f}$   conservation of charge:  $Q_1' + Q_2'= Q_1 + Q_2$,        $C_{eq} =$ $\frac{Q_1 + Q_2}{V_f}$  $V_f = $$\frac{Q_1 + Q_2}{C_1 + C_2}$  The initial energy of the capactiors is:  $U_0 = $$\frac{Q_1^2}{2C_1}$$+\frac{Q_2^2}{2C_2}$  $U_f = $$\frac{1}{2}$$(C_1 + C_2)V_f^2 = $$\frac{(Q_1 + Q_2)^2}{2(C_1 + C_2)}$  $\Delta U$$ = $$\frac{(Q_1 + Q_2)^2}{2(C_1 + C_2)}$-$\frac{Q_1^2}{2C_1}$$-\frac{Q_2^2}{2C_2}$  However, I don't see how this is necessarily non-negative.