Plate Definition and 960 Threads

I learned about Bessel functions and steady-state temperature distributions in the past. Recently, I was searching online for some example problems on the topic and found the "original question" along with the solution online as a PDF file. While I am unsure will it be appropriate for me to...

a)$$C=\frac{\kappa\epsilon_0\ell x}{d}+\frac{\epsilon_0\ell(\ell-x)}{d}=\frac{\epsilon _0ℓ\left(\kappa x+ℓ-x\right)}{d}$$ b)$$U=\frac{1}{2C}Q^2=\frac{dQ^2}{2\epsilon _0ℓ\left(\kappa x+l-x\right)}$$ c)$$F=-\frac{dU}{dx}=\frac{dQ^2\left(\kappa -1\right)}{2\epsilon _0ℓ\left(\kappa...

I don't really understand the question. I don't understand the wording. We know the plate has a thickness L = 0.50cm. If the charge is coming from the battery wouldn't the electrons have to move the entire distance to reach the face of the plate? Because they have to move all the way from the...

Hi, in the Timoshenko’s book "Theory of elastic stability" one can find a case of simply supported rectangular plate uniformly compressed in one direction (compressive load is applied to shorter edges). The formula for critical load is: $$N_{cr}=\frac{\pi^{2} D}{b^{2}} \left( \frac{b}{a} +...

Potential depends on the charge contained by the conducting plate. So the plate C should change the electric field and hence potential on both plates A and B. This should change the absolute value of potential,but since A and B are still connected to that cell, I think the potential difference...

Homework Statement:: n/a Relevant Equations:: n/a Sorry for the wonky mouse sketching. Teacher said that arrows must touch the plate at the other end. Is there actually such a thing or is this just preference? I thought convention was for arrow to be in the middle of the line.

(a) (b) have intuitive solution but the asymmetry in (c) is confusing.

Summary:: Griffiths problem 8.5 Problem 8.5 of Griffiths (in attachment) I already solved part (a), and found the momentum in the fields to be $$\textbf{p}=Ad\mu_0 \sigma^2 v \hat{\textbf{y}}$$ In part (b), I am asked to find the total impulse imparted on the plates if the top plate starts...

Bit of a random question... capacitors can be a bit weird, in that if we connect one up to a source of EMF and do positive external work to separate the plates of the capacitor, the energy of the capacitor decreases (and instead the work you do plus the decrease in capacitor energy goes into the...

In order to find force( and hence the Acceleration) on the Pentagonal plate,we must find the Resistance of the plate.But to find the resistance we must know how the current is flowing through the given plate(see attached figure). My question is how is the current flowing through the Pentagonal...

I used to work with invasive species in the early 2000's. I saw firsthand the damage a single invasive species can wreak on an ecosystem (Emerald Ash Borer among other insects.) After watching videos of plate tectonics, I began to wonder what would happen to ecosystems on large scales during...

I found out the equation of electric potential, that is V=\int_{-a}^a \int_{-a}^{a} \frac{σdxdy}{4 \pi \epsilon_0\sqrt{x^2+y^2+d^2}}=\int_{0}^a \int_{0}^{a} \frac{σdxdy}{\pi \epsilon_0\sqrt{x^2+y^2+d^2}} but I couldn't calculate the integral. It seems convenient if we use the polar coordinate...

I'm 3d-printing a part that is 110mm x 40mm (XY-plane). I have to keep it light weight, so I made it thin - 0.6mm (Z direction) and filled the surface with holes to remove as much weight as possible. Then I added a grid of 2,5 mm high "walls" in the XY directions to make it stiffer and a couple...

I have a question and searched about at google and found an answer which I don't make sure. If there is 26 letters and 10 digits; my answer is: first letter: 1 way(which is A) second letter: 26 way third letter: 26 way first digit: 1 way(which is 1) second digit 1 way(which is 2) third digit: 10...

This is the problem I'm working on. So far I know: 1. I am assuming the free charge density is +sigma for the top plate and -sigma for the bottom plate. 2. The electric field from the plates goes from top to bottom plate, in the negative z direction. 3. The electric field of the capacitors...

1. Can I use the surface charge equation: $$Q = \frac{Vk\epsilon_0A}{d}$$ Where V = Voltage, k = dielectric constant, ϵ0 = permittivity of free space , A = Area of plate and d = distance between plates. For a conductive plate within an electric field? My thinking is that if the plate is...

Here is the image of the problem. I arrived at the solution that the force on MN is in fact 100lbs due to P2 because the components P1 and P3 acting along MN are equal in magnitude but opposite in direction. What I don't understand is why the force is acting in the direction OPPOSITE to...

In the following cross section, the static guide plate (light blue) is rigidly constrained, fixed to the body (not shown) of the mechanism. It serves as the mounting point for a cranked axle (dark blue) via a combination thrust and radial bearing (pink & yellow) that constrains it to a single...

If I put a very long steel plate above a coil with DC, the magnetic field above the plate will decrease because of the shielding of the steel plate. However, from the perspective of magnetci domain, some domains will be magnetized to turn to the direction of the magnetic field from the coil...

Homework Statement:: If you have a 1" thick steel plate (A36) with a 1.125 hole (supported at 3" half way around), what is the maximum weight that a 1" grade 8 bolt can support using a 2 to 1 safety factor. The weight is applied directly the the bolt Relevant Equations:: dunno? it's been 24...

Hello, First of all, I hope this post is in the right section (aerospace engineering). I am doing research on the injector plate design for a hybrid rocket and I'm no where at the moment. I was thinking that I could improve the geometry of the injector plate in order to help improve some...

So, I was studying about general properties of matter and topics like surface tension. I came across the phenomenon of water rising along a glass plate like in the picture. I looked for some mathematical interpretation of this on the internet and in some books. [![enter image description...

Merged thread deleted first post next post is the first post.

i need a simple calculation of a stirling ltd surface area calculation per watt produced and would a very rough surface and very large surface area hinder heat flow if the distance to re generator is extreme /would folding the surface area of a flat plat ltr help increase the power of engine...

The question is partially taken from Griffith's book. I am confused about the physical meaning of momentum in fields. I have determined the solution and found that in part d the momentum crossing the x-y plane is some value in the positive z direction. I don't however understand the physical...

I tried to find the the Electric field due to the image charge. So the potential due to the image charge is V=-(pR^2)/√(4R^2-4rRcos(θ)+r^2). When I took the gradient of that in spherical coordinates, I got a mess that doesn't seem to be possible to integrate.

$$C=K\varepsilon_0\frac{A}{d}=C=\frac{(8.85\times10^{-12})\times1\times 0.0254469}{0.01}=0.000022531F=22.531μF$$ 6V*(1-2.71828-t/0.019Ω*0.0000225307uF) time constants 6*(1-2.71828-1) = 6*(0.632) = 3.79 sec 6*(1-2.71828-2) = 6*(0.865) = 5.18 sec 6*(1-2.71828-3) = 6*(0.950) = 5.70 sec 6*(0.982)...

Consider a plate capacitor with a dielectric interface (\epsilon = \epsilon_0*\epsilon_r, thickness=d) tilted at the angle \alpha . Outside the interface \epsilon = \epsilon_0. Without dielectric interface is the field \vec{E}=E_0*\vec{e_z}. Determine the E-field inside and outside the...

Here are my workings, and I was wondering if I'm correct so far. Let ##m## be mass of bullet and ##M## be mass of plate. COM: ##mu_{bullet} = (m+M)v## ##\frac{1}{2}(m+M)v^2=(m+M)gh +\frac{1}{2}I\omega ^2## where I is the inertia, so using parallel axis theorem, ##I = \frac{1}{12}bh^3 + md^2 =...

Hello, A question came up in my head that I couldn't think of a way to math out. Say I want to design a parallel plate capacitor. The equation for capacitance is quite simple: Everything in this equation makes sense, besides for the distance. This is saying that an infinitely small length...

I've been given this question for my TMA2, I've tried looking at the learning material but it gives no information on how to calculate the gap? Does anyone have a formula for this? Or can someone point me in the right direction? Thanks

Hello All, I am working on a project with plate heat exchangers connected in a cascade system to heat up water connections in a huge system The Problem Statement : A boiler produces and circulates hot water at 65 degC to a Heat Exchanger and come out at 50 degC, where as the other fluid is...

I have calculated KE_i and KE_f, took the difference between the initial and final kinetic energy of the bullet to be equal to the work spent to overcome the friction, and divided it by the distance traveled, but arrive at around 20000N. The solution should be 9.5*10^7. Not sure what else to...

I know that the field inside sample is a combination of the demagnetizing field and whatever applied field you may have. So these two fields together influence how big a field you need in order to magnetize the sample.

I am trying to solve the following problem: My attempt at the problem: $$m = 9.11 * 10^{-31}kg$$ $$q = 1.6 * 10^{-19} C$$ $$V_0 = \sqrt{\frac{2KE}{m}} = \sqrt{\frac{2 * 1.6 * 10^{-17}}{1.6 * 10^{-19}}} = 5,926,739 m/s$$ $$F_{net} = -F_{e} = ma$$ $$a = \frac{-F_{e}}{m} = ma$$ $$E =...

So I figured to get e-field at point (4,4,0), I need to find the resultant e-field from the negatively charged particle and the plate ##E_{resultant}=E_{particle}+E_{plate}## ##E_{particle}=\frac{kq}{d^2}=\frac{(9*10^9)(-2*10^-6)}{4^2}=-1125N/C## Now for the plate is where I'm confused. If this...

i have a neobydium magnet of grade n40 , the diameter of magnet is 15mm and thickness is 10 mm , now i want to calculate the pull force between this magnet and a steel plate when there is no gap between them ; & in second case i want to calculate the pull force when i put a 0.15mm copper plate...

the radius of the hole should decrease from my perspective but the book says that the radius of the hole will increase. I am not able to understand why??

Thinking of building a vibrating compactor to compact dirt and gravel for a new driveway section. I already have a horizontal shaft 13 horse honsa engine. I have some scrap steel. My question is concerning the exiter/vibrator. I was thinking of mounting 2 pillow block bearings with a pipe. A...

Hello, I have a question regarding the capacitor/resistor network as shown. My question is simple. I realize that the instant the switch is closed, then the top plate of the capacitor must be at a potential (VA) of 5v. However, I also realize that the instant the switch is closed, literally...

Question as follows: My answer/explanation: Force needed to make block slide = static friction between block and plate. So friction = normal of block * static friction = (0.5∗9.8)∗0.9=4.41N(0.5∗9.8)∗0.9=4.41N My thoughts/wrong answer probably?: after block slips, plate experience kinetic...

Problem Statement: How to calculate minumum angular velocity of a mass on a spinning plate Relevant Equations: f=mrw^2 Hi, here's the question: a) A rough horizontal plate rotates with a constant angular velocity of w about a fixed vertical axis. A particle of mass m lies on the plate at a...

Tried to find the resultant force, but I can't see how the magnetic field affects. I used Faraday's law to find the the diferece of potentials in the plate Wich should be B.d.v, where v is the vertical velocity of plate, but there were not given the resistance or resistivity to relate with the...

Summary: damage on glasses plate by hitting ball If a ball hit a rectangular plate of glass and it cause a damage "but it didn't broken" how can i represent this damage using mathematics? I'll tell you my idea about it: let the ball move horizontally and hit the plate perpendicularly with...

The plate is in inclined position in a chamber where the air flows from bottom to top.

I am trying to come up with a design for a device with which to generate a rapidly pulsed proton beam (on the order of 1 pulse per ms). My thought was to apply a 10 kV potential between two parallel plates (each with a hole in their center) and inject a steady stream of hydrogen gas through the...

The problem of the interaction of a point charge with a dielectric plate of finite thickness implies the existence of an infinite series of image charges (see http://www.lorentzcenter.nl/lc/web/2011/466/problems/2/Sometani00.pdf). I introduce notations identical to those used in this work. The...

Suppose there exists a pair of parallel plates with a voltage between them. These plates have a certain amount of energy stored in the electric field between them (E=1/2*C*V^2). Now we fire a fast (~5,000,000 m/s) beam of protons through the plates (parallel to the electric field) such that the...

My question might sound stupid to you but please clear my confusions. I'm taking an circular arc like element on the plate. That arc has a radius of 'r' (AB) and the radius is inclined at an angle 'θ' with OA (∠OAB). The area between arc of radius r and r+dr is dA. dA = 2θr.dr The charge on...

Hi all, I need to convert a cooling fixture from a weighted system to a plate and bolt system. I'd like to use 4 - 10mm cap screws and a pressure plate to replace 7.82kg of weight. The weights are 190mm x 70mm of contact area. The pressure plate will have flanges to accommodate the bolts...