We've done something like this before haven't we? The trick is expand each plate into the sides of two capacitors. I can draw a diagram if that's not clear.
@Abcd Each plate behaves as if its two sides are part of a capacitor with spacing $d$. In the lower diagram I've shown this by expanding each plate into an H shape. I've coloured the plates to try and make it clear how the top diagram expands into the lower one.
Consider the following system:
I am thoroughly confused about certain aspects of the situation described in this diagram in which a block is placed on a wedge inclined at an angle θ. (Assume no friction everywhere)
Let us consider a few different cases:
Firstly, when the wedge is accelerati...
@harambe The vertical acceleration of the block $z$ is the same for an observer standing by the wedge because the wedge does not move in the vertical direction. That observer would see the wedge accelerate at $X$ to the right and the block accelerate a little faster at $x$ to the right. Remember the block is accelerating down the incline. So acceleration of the block relative to the wedge is $x-X$ to the right. — Farcher1 hour ago
The wedge frame and lab frame observers have different horizontal accelerations, so in their frames the horizontal component of the block's acceleration will be different.
But, both the wedge and lab observers have zero vertical acceleration. So in both the wedge and block frames the vertical component of the block's acceleration $a_v$ must be the same.
@Abcd As with the problem in Physics Q&A, you can use the Conservation of Energy to find heat produced or work done by external agent. The Stack Exchange answer will help you.
@sammygerbil Okay, leave my solution... Could you please tell me what is to be done in the above question? I am not able to infer much from that SE answer
:45696372 Part (ii) here is the same kind of question : dielectric slab inserted while battery connected. Could you post your question and your answer on the Physics Q&A site? I have difficulty working on this in chat.
the fringe electric field force and the external agent force
since accceleration is 0
both forces should be equal and opposite
Work done by all forces = Change in kinetic energy // Work Energy theorem
Work done by external agent + Work done by fringe electric field + Work done by battery force + Work done by resistive forces = Change in kinetic energy = 0
Now work done by external agent= -ve of work done by fringe electric field
Work done by battery force = EMF $\times\Delta Q = CV^2 (K-1)$
Work done by resistive forces goes in the form of heat
The battery is doing the work done by the fringe electric field. I don't know what the "resistive forces" are. Isn't that the force supplied by the external agent?
The way I look at it is that the capacitor is "the system". The battery does work on "the system" equal to QV. The system does work on the external agent equal to QV/2, and is left with extra internal energy QV/2.
The question does not ask for heat produced in step (ii). Maybe that is what is confusing you - it confuses me. It is not clear to me whether the same "resistive force" (ie resistance in the wires) is still present when the external agent does work in step (ii).
Considering the potential $\psi(r)$ of a sphere with density $\rho(\mathbf r')$,
connected by a small volume positioned in the $P'$ point as shown in the figure:
The $\psi(r)$ is:
$$\begin{align}
\psi(r)=-G\iiint_{\mathcal{V}} \frac{\rho(\mathbf r')dx'dy'dz'}{|\mathbf r - \mathbf r'|}=
-G\i...
As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including:
ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room.
An altern...
Damn, if you faced difficulty because of mathjax, I am very sorry, I should have told you about this earlier.
Sorry I have to go in 7 minutes. If you get my error please ping me
Consider the following system:
I am thoroughly confused about certain aspects of the situation described in this diagram in which a block is placed on a wedge inclined at an angle θ. (Assume no friction everywhere)
Let us consider a few different cases:
Firstly, when the wedge is accelerati...
Considering the potential $\psi(r)$ of a sphere with density $\rho(\mathbf r')$,
connected by a small volume positioned in the $P'$ point as shown in the figure:
The $\psi(r)$ is:
$$\begin{align}
\psi(r)=-G\iiint_{\mathcal{V}} \frac{\rho(\mathbf r')dx'dy'dz'}{|\mathbf r - \mathbf r'|}=
-G\i...
As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including:
ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room.
An altern...
