Plane Definition and 1000 Threads

Hello,There is a model which tunes a plane wave using certain expressions which resembles the spherical to cartesian coordinates. There are two types of definitions: propogation normal and electric field vector. Why they put in propogation normal exactly the spherical to cartesian to represent...

Can someone prove that outside of two infinite planes with opposite charge, the E-field got cancelled? But the between are not.

The (covariant) product of the EM Field Tensor with itself is basically the Lagrangian Density for the EM Field. It leads directly to Maxwell's Equations. If there are no charges or currents present, Maxwell's Equations lead directly to an equation of motion for an EM Plane Wave. Now all EM...

I am currently trying to make a game about Saturn and came across the xkcd article about the Interplanetary Cessna. Could their assessment of Saturn's atmosphere be incomplete in this context? Saturn has a relatively dense atmosphere, even tho its mean molecular mass is just 2.07. At the...

In my line i have, ##\dfrac{∂r}{du} = \vec{i} +\dfrac{1}{2}u \vec{k} = \vec{i} +1.5 \vec{k}## ##\dfrac{∂r}{dv} = \vec{j} -\dfrac{1}{2}v \vec{k} = \vec{j} -0.5\vec{k}## The normal to plane is given by, ##\dfrac{∂r}{du}× \dfrac{∂r}{dv} = -\dfrac{3}{2} \vec{ i} + \dfrac{1}{2}\vec{j}+\vec{k}##...

The question is a problem from Leithold's calculus book. I didn't understand the (x = 5 \cos(t)). Shouldn't it be (x = 2 cos(t))? I'm referring to item b. i tried this way. i don't know what is wrong.

I want to know that if I place light sources on the plane perpendicular to the principle axis of the cylindrical lens, do all light beams diverge in the same way? Assume all light sources are lasers of having same wavelength and beam divergence Also how extent can i minimize interference?

My attempt: The shape of the hyperboloid would be like this: If the hyperbolod is cut by plane z = d, the intersection would be a ellipse. Projecting the intersection to xy - plane, I think I get: $$-2\leq x \leq 2$$ $$-b\sqrt{1-\frac{x^2}{a^2}} \leq y \leq b\sqrt{1-\frac{x^2}{a^2}}$$ So the...

Snapshot of Mary L. Boas' Mathematical Physics book So, the marked lines say `If we think of P as the point z = x +iy in the complex plane, we could replace (2.3) by a single equation to describe the motion of P` But, until now I have only learned of representing points in the form (x,y), now...

I just don't understand should I take u relative to the plane or relative to the ground. I tried to solve it like this: $$p_{final}=m_{0}v-m(u-v)-M(u-v)$$ $$p_{initial}=m_{0}v$$ $$\Delta p=-m(u-v)-M(u-v)$$ ##m_0## is mass of the plane. $$F=\Delta p$$ $$F=-m(u-v)-M(u-v)=(m+M)(v-u)$$...

I want to use the Lagrangian approach to find the equation of motion for a mass sliding down a frictionless inclined plane. I call the length of the incline a and the angle that the incline makes with the horizontal b. Then the mass has kinetic energy 1/2m(da/dt)2 and the potential energy should...

The answer key is the light is directed through one polarising filter then filter is rotated and the light changes intensity. I don't understand how that proves that the light is plane polarised. I think if the light is unpolarised, the intensity will also change when it passes through...

Hi, i'm trying to solve this problem. It's exercise 3 on page 5 from this book: Challenging mathematical problem with elementary solutions The solution is on page 41: I'm OK with the 4 circles in case 1: i can pick (inside/outside): ABC + D, ABD + C, ADC + B, BCD + A. What i cannot...

The other day I was down at the dock and I heard an aircraft coming up from behind. I didn't look up right away but it caught my ear because commercial jets don't fly that way (westward, from the small island airport). I looked up as it passed over, a thousand feet up or so, expecting a 707 or...

The virtual displacement should be given by $$ \delta\vec{r} = \begin{pmatrix} \cos(\alpha) \\ \sin(\alpha) \\ \end{pmatrix} \delta s $$ where ##\delta s## is a displacement parallel to the plane. The relevant force should be the gravitational force, as given above. Thus, the equations of...

Hi all, I am a beginner in Linear Algebra. I am solving problems on vector spaces and subspaces from the book Introduction to Linear Algebra by Gilbert Strang. I have come across the following question: Suppose P is a plane through (0,0,0) and L is a line through (0,0,0). The smallest vector...

Hello. For a project I am working on I need to draw a template of a "curve of intersection" of a plane (B) intersecting a cylinder at a "compound angle".. I do not know the correct terminology so I added a sketch of what I wish to achieve. If it is not understandable please say so and I will...

Problem: I have done part a) in spherical polar coordinates. For part b) I thought it would be just: $$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$ But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...

Is it results in a new shockwave or does the shockwave continuously created by hypersonic flight suddenly disappear? I guess slowing down from hypersonic speed will cause a lot of vibration on the plane.

Hi everyone I have worked solutions to the question, but I don't fully understand what they are doing and I get a different answer. I used d=|PQ*n| and chose (0, 0, -7/2) as a point on the plane. I got that point by letting i and j = 0. Since P = (1, 1, -1), PQ = (-1, -1, -5/2). The...

a = 9.8*sin(25*pi/180)=>a=4.1417 m/s^2 vf^2=vi^2+2*a*s=>vf=sqrt(0^2+2*4.1417*3)=>vf=4.9850 m/s Meanwhile the correct answer is: (vf+vi)/2=>(vf+0)/2=2=>vf=4 m/s Why is my answer wrong? It seems that the acceleration is what is wrong, but I don't understand why.

Hi, I want to solve the problem by method of mirroring and by using the electric field by doing superposition and then adding them up to use in Lorentz law to get the force. I have attached a figure that represents the problem. How do I know from the figure that $-p_l$ is from the...

One of the strange features of Quantum Mechanics is that for his formulation one needs the classical physics that actually should emerge as its macroscopic limit. All experiences with quantum objects have to be analyzed through classical "glasses". Naturally, then the question arises: where...

Why in order to derive the QM momentum operator we use the plane wave solution. Why later on in field theory and particle physics, the plane wave ansatz is so physically important?

Hi everyone One of the numbers in my attempt would hint that I have gotten something backwards in this question, but I can't see how. For the plane 3x + 2y -z = 4, I've assumed the vector form is r⋅(3i+2j -k) = 4. That is, (3i+2j -k) is the normal to the plane. That being so, (3i+2j -k)...

1- Coordinates of two points are given in x and y plane. A(x1,y1), B(x2,y2) Calculate the angle between the two lines passing through each of these points with the origin of linear coordinates. 2- If a line passes between the two points A and B above, does point C lie on this line? C(x3,y3) how...

As the title asks, does the invariable plane of the Solar system have axial precession? And if so, how much and at what rate? I have tried to find an answer to these questions for a while now, but still haven't found any. I recently asked on reddit too, which pointed me to some speculation...

For part(d) of this problem, The solution is, However, how did they know that the object moves in a circle of radius 5.00m centered at (0,4.00m)? Many thanks!

For this problem, How do we calculate the moment of inertia of (2) and (3)? For (3) I have tried, ##I_z = \int r^2 \, dm ## ## ds = r ## ##d\theta ## ##\lambda = \frac {dm}{ds}## ##\lambda ## ##ds = dm ## ## \lambda r ## ##d\theta = dm ## ##I_z = \lambda \int r^3 d\theta ## ##I_z = \lambda...

I have a flat planar part made of crystalline sapphire (about ~2k weight, and polished to a mirror finish) that rests on three ball bearings, and I want to minimize the static friction at these 3 interfaces. The ball bearings are fixed so they cannot roll, and the sapphire part can only slip...

For part (c) of this problem, My working is However, the tricky part is to find theta. I tried to draw the situation so that I could find theta: It appears that theta = 90 degrees. However, this does not seem to be correct. Does anybody please know how to correctly find theta in terms of...

I am stuck on Question e and then how to proceed to f. I cannot seem to show this using the steps in the prior questions. My answers are: a) b) c) c) continued - and d) at the bottom of the page d)I am not sure where I have gone wrong, as I am not sure how to apply the relevant...

hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...

I was looking at an example of fluid mechanics and I don't understand this. Statement figures: CONTINUITY EQUATION $$\left. \dfrac{dm}{dt}\right]_{MC}=(\dot{m}_2+\dot{m}_3)-\dot{m}_1=0$$ $$\dot{m}_1=\dot{m}_2+\dot{m}_3$$ $$\rho c_1A_1=\rho c_2A_2+\rho c_3A_3$$ $$\rho c_1 h1=\rho c_2 a1+\rho...

I - A point divides a line into two parts; II - A line divides a plane into two parts; III - Does a smaller sphere divide a larger sphere into two parts, like layers of an onion? Note that the first two statements, the question of infinity must be considered. For the third statement, is the...

Suppose an optical scalar wave traveling in Z direction. Using the diffraction theory of Fourier Optics, we can predict its new distribution after a distance Z. The core idea of Fourier Optics is to decompose a scalar wave into plane waves traveling in different directions. But this...

So i am tried to conserve momentum and use conservation of mechanical energy but won't there be psuedo force acting on the block if i am solving from non inertial frame ?. If i ignore the pseudo force and simply use C.O.M.E and include the K.E of the wedge and solve normally i do get the...

So the question was if a plane is going from point A (origin) to point B 400 km directly south of point A at 220km/hr north and there is a wind going 62 km/hr east to west, what angle should the plane orient to go straight from point A to point B? I got something lik 16.4 degrees. The second...

This is a homework problem of my grand daughter. The question is to find out the conditions of an object M on a slope with angle shown and applied force "F". I find there are 3 conditions, sliding up, sliding down and not moving. This is my work. I just want to get comments on my work: At the...

I was thinking about how various objects would slide down on an inclined plane, and I just couldn't figure this problem out. So let's say I have this screw or cone on its side, on an inclined plane. If friction exists, what would the motion of the screw be as it slides down the inclined plane...

I know the normal of plane ABQP is -2i - j + 3k but I don't know how to prove that 2i + j + 3k is the normal vector of plane CDPQ Thanks

What mechanism pulled small ice and stone particles preferentially into orbiting in the equatorial plane of Saturn? Is there a resonance involved? Wikipedia says that there is no consensus. What are some hypotheses?

Hi everyone. I came across the following brainteaser: A plane travels from airport A to airport B and then returns to A from B. There is no wind, both trips follow a straight line, and the plane flies at constant engine speed. Suppose now that a constant wind is blowing from A to B. Will the...

Since the snails are all in the same plane and their paths are not parallel, shouldn’t the solution simply be yes since the non-parallel lines in the same plane will intersect at some point? This answer seems too simple so I’m unsure if I‘m missing out on a detail.

Suppose a square lattice. The planes are such as the image below: I light wave incides perpendicular to the square lattice. The first maximum occurs for bragg angle (angle with the plane (griding angle) as ##\theta_B = 30°## (blue/green), green/blue in the figure). The angle that the...

I'm reading an article about the order-chaos-order sequence of a spring pendulum [Ref 1], as I'm reading it I'm trying to reproduce the graphs and results through Mathematica. However, I am new to this software. I will list below some of the most important equations mentioned in the paper. "In...

Hello, I need a bit of help. My age and fading competence are showing (no complaints, just facing up to it). I have an optical SETI observatory in Panama with a 20" Newtonian and a piggybacked 14" Cassy. I wish to mask a portion of stellar Airy disks with an E-W wire on a small photometer...

Textbook examples usually involve a plane monochromatic wave that is diffracted by a plane grating. If one places an ideal focusing lens behind the grating one will get a diffraction pattern in the back focal plane of the lens. The geometric size of this diffraction pattern is proportional to...

Summary:: I'd like to check my understanding of standard problems where a billiard ball resting on a plane is hit horizontally at some height above its center So the situation is that a ball of mass ##m## and radius ##r## is at rest on a horizontal surface. There is friction between the ball...