Point Definition and 1000 Threads

So, the way I understand this problem, I think the line ##y = (2/5)x + c## should only intersect some of the circles drawn around the lattice points. But, I am not sure I even understand the problem statement. Can the line pass through the lattice points ? My first goal is to understand the...

$$f(x,y)=\left\{\begin{array}{ccc} (x^2+y^2)\sin\left(\frac{1}{\sqrt{x^2+y^2}}\right) & , & (x,y)\neq (0,0) \\ 0 & , & (x,y)=(0,0) \end{array}\right.$$ This function is differentiable at (0,0) point but ##f_x## and ##f_y## partial derivatives not continuous at (0,0) point. I need another...

My problem is on how to arrive at ##d=\dfrac{mx-y}{\sqrt{1+m^2}}## My working steps are as follows; ##d^2=(x_1 - x)^2+ (y_1-y)^2## ##d^2=(\dfrac{y}{m} -x)^2+ (mx-y)^2## ##d^2=\dfrac{(mx-y)^2}{m^2} + (mx-y)^2## ##m^2d^2=(mx-y)^2(1+m^2)## ##d=\dfrac{mx-y\sqrt{1+m^2}}{m}## ...unless they...

On Problem 3.11 for Griffiths' Electrodynamics, there is a question that asks for the critical value between a point charge and a conducting shell, but I don't quite know what they mean by 'critical value' in this context and how I'm supposed to approach this question, the rest of the problem is...

Since ##x## is larger than the linear dimensions of the cylinder, hence it can be approximated to be a point dipole . $$\vec{F}=\left(\vec{\nabla}\cdot \vec{p}\right)\vec{E}$$ In our case : $$\vec{F}=p_x\frac{\partial E_x}{\partial x}$$ $$F=\frac{-2kQp_x}{x^3}$$ Of course , we can assume some...

Question : I have tried to solve but I struggle with this part: Any help would be appreciated.

I want to ask about the direction in which ##D_v## is zero at point (1, 2, 1) My attempt: $$w_x=yz+\frac{1}{x}$$ $$w_y=xz+\frac{1}{y}$$ $$w_z=xy+\frac{1}{z}$$ At point (1, 2, 1), the ##\nabla w=<3, \frac{3}{2}, 3>## $$D_v w=0$$ $$\nabla w \cdot v=0$$ $$ \begin{pmatrix} 3 \\ \frac{3}{2} \\ 3...

I've no idea how to solve this problem. The sign of the charge is not mentioned, so I'm assuming the charge is "+". The charge exerts an outward electric field. Since two lengths of the right-angle triangle are given, I use the Pythagorean to find the hypotenuse, which is the distance between q...

There are two identical spheres with the same charge that are the vertices of an equilateral triangle. ##+3 \mu C## will exert an outward electric field, which is drawn in the FBD below (see the attached pic), Since the horizontal force components (1x and 2x) are equal and opposite at point P...

As the observer is moving, there will be a magnetic force. Electric Field of the Rod = λ/2πεr r̂ Electric Force on the Point Charge = qλ/2πεr r̂ Magnetic Force on the Point Charge = q(vxB) = qvB n̂ = qv(µI/2πr) n̂ = qv(µλv/2πr) n̂ = µqλv²/2πr n̂ Total Force = Electric Force + Magnetic Force

The total force acting on the pulley is zero so: F=mg+T1+T2 (1)Analyzing the torque and angular acceleration about the actual axis of rotation, the axle of the pulley, gives: τnet=T1R−T2R=Iα (2)If we analyze about point P, the right edge of the pulley where T1 is applied, we get...

##\hat a_B=\frac 2 3\hat a_x-\frac 2 3\hat a_y+\frac 1 3\hat a_z## ##\left| \vec r\right |=\sqrt {(x_B-6)^2+(y_B+2)^2+(z_B+4)^2}=10## ##\left |\vec A\right |=\sqrt {6^2+2^2+4^2}=\sqrt {5}{6}## Not sure where to go from here. Please help! Source: Problem 1.3; Engineering Electromagnetics, 8th...

[Mentor Note: See post #10 below for an updated problem statement using LaTeX and with a better drawing] what i want is to find the axis of rotation when the centre of gravity and point on which external force is acting is given along with the magnitude and direction of force. In the example...

Problem: Solution: This was quite simple, are my solutions correct?

Hi, unfortunately, I am not sure if I have calculated the task correctly The electric field of a point charge looks like this ##\vec{E}(\vec{r})=\frac{Q}{4 \pi \epsilon_0}\frac{\vec{r}}{|\vec{r}|^3}## I have now simply divided the electric field into its components i.e. #E_x , E-y, E_z#...

TL;DR Summary: Please Help. I need an answer for an Investigation if a uniform bar of length 2200mm is supported evenly on 2 points (1 and 2) 1190mm apart. The bar is comprised of 3 sections (A, B and C) of varying masses. Section A and C have equal mass and volume and is comprised of the...

There are components of 500N: 500cos(45)= 353.55 500sin(45)= 353.55 Radius is 3 then M = (353.55*5.12) - (353.55*2.12) = 1060.65is that correct?

This is the figure stated for problem 57.

I've look if there was any way to get the "image size" or a ratio to use the Mirror Equation to find the focal length, but nothing. I think it's base on some geometry, but I don't see the relation.

I reasoned that at the coin's slowest velocity, the energy it has must just be enough for it to reach the highest potential configuration: when the point mass is directly above the centre of mass of the coin, and its GPE is ##mg(R+r)##. I used this to find the minimum velocity, but I can't think...

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...

I did not use the hint for this problem. Here is my attempt at a proof: Proof: Note first that ##σ(σ(x)) = x## for all ##x \in G##. Then ##σ^{-1}(σ(σ(x))) = σ(x) = σ^{-1}(x) = σ(x^{-1})##. Now consider ##σ(gh)## for ##g, h \in G##. We have that ##σ(gh) = σ((gh)^{-1}) = σ(h^{-1}g^{-1})##...

If these point charges were placed in vacuum without any spherical shells in the picture, then the force between these charges would be ##F =\dfrac { k q_1 q_2} {d^2}##. But, I am unable to reason how spherical shells would alter the force between them. I do know that if charges were on the...

Hello everyone! I'm trying to replicate phonon density of states (PHDOS) diagrams for some solids using Quantum Espresso. The usual way I do it is the following one: scf calculation at minima (pw.x) Calculation of dynamical matrix in reciprocal space with nq=1 or 2 (ph.x) Calculation of...

Seems a crazy coincidence that the tiple point of water is also virtually the same temperature at which water freezes/melts. Or is it that the triple point of water was always going to be at the temperature that water freezes/melts (so those two neccessarily co-exist) and then above water there...

I'm having trouble understanding how to find out whether or not a stationary point is a minimum and I'm hoping for some clarification. In my class, we were shown that, using Euler's equation, the straight-line path: with constants a and b results in a stationary point of the integral: A...

Since the electric field due to a conducting plate is twice the electric field due to a plastic plate having same charge density, the electric field at the point P will be twice in case of conducting plate and hence it is 20 volt per metre. Is that correct?

A solution was provided: We take torques about point B. Note that τ = MgL/2 = Iα so α = (3g)/2L. Everything from here is straightforward. I don't understand why in this step, you can take torque about B without accounting for a fictitious force due to the acceleration of the Rod.Thanks for...

I tried using the distance between r2 and r1 and plugging them into the equation for i, j, k. >> So for the force in the x direction it was k*(4E-6*4E-6)/(4-9)^2. The answer I got was wrong according to webassign. Can someone please tell me what I am missing?

My issue is in deriving the coordinates of a point on a wheel that rotates without slipping. In Morin's solution he says that: My attempt at rederiving his equation: I do not understand how the triangle on the bottom with sides indicated in green is the same as the triangle on top that is...

I am struggling with part b of the question attached in the screenshot. For part a, I simply add the components of the given forces. I tried calculating the moments using vector cross multiplication, but I don't know what to do after that or even if that step is useful.

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...

I think I read somewhere that the trajectories of particles in the De Broglie–Bohm theory do not cross, is that true? If true, then in the case of Rutherford scattering the trajectories below can't be those of the De Broglie-Bohm theory? Thanks.

High School Physics Lab: Take 200mL of water (Room temp) and place it in a microwave on high for 60 seconds. Calculate the Energy transferred to the water by the microwave. Pretty easy: Step 1: Heat of Temp Change : Q= mC∆T where m=200mL Step 2: Add Heat due to phase change: Q=mL where m=...

When two free jets collide at some impingement angle (not necessarily a head on collision), the usual assumption is that in the impingement zone there is a stagnation point around which stream lines are deflected. From this stagnation point, a thin liquid sheet is created, which eventually...

M 6.4 - 12km WSW of Ferndale, CA https://earthquake.usgs.gov/earthquakes/eventpage/nc73821036/executive 2022-12-20 10:34:25 (UTC) 40.523°N 124.393°W 16.1 km depth https://en.wikipedia.org/wiki/Juan_de_Fuca_Plate#/media/File:Juan_de_fuca_plate.png Numerous aftershocks (Mag 2-4) occurring...

Why when you integrate the Biot-Savart Law do we not include limits of integration on the left-hand side of the equation (for the differential magnetic field)? Would the lower limit be 0 and the upper limit be B? How would you tell? Many thanks!

My approach; ##v=u+at## ##0=12-3t## ##t=4## i.e at point when deceleration starts up to the point cyclist stopped (point ##B##). Therefore, distance travelled in the ##4## seconds is given by, ##s=(12×4)+(0.5×-3×16)=48-24=24##m ##⇒240-24=216##m ##t=\dfrac{216}{12}=18 ##seconds...

but for me there is no solution to this inequality... I never wait for a ready answer but I've already spent 4 hours on it and I still don't know what to mark...

>>> from numpy import exp, pi >>> exp(1j*pi) (-1+1.2246467991473532e-16j) The fact that the imaginary part of this is not zero is wrecking a fourier collocation scheme for a nonlinear PDE with periodic boundary conditions: the coefficient corresponding to the Nyquist frequency, which should be...

I tried solving it and i was able to do a) and b) here is what i did on c), but its not correct according to the solution

Suppose we have an expanding sphere. That means that the surface ##4 \pi r^{2}## is getting bigger and bigger. For example, suppose the area expansion rate is ##b \, r##. Does this limit the speed at which a point can move on the surface?

Hi, unfortunately, I'm not that fit concerning the Lagrangian formalism, so I'm not sure if I solved the problem 1a correctly. I have now proceeded as follows the Lagrangian is $$L=T-U$$ Since there are no constraining or other forces acting on the point mass, I assume that the...

Since the question made no indication of the disk rotating about its center, I just straight up assumed that the disk did not rotate about its center, and instead treated it as a point mass. However, to my surprise my calculations did not bear me any fruit. Below is my first attempt at the...

The net torque about an axis through point A is given by, If I take the axis of rotation perpendicular to the paper and the solution I arrive would be the following below Net torque = 30 cos45 x 1.5 - 10 cos30X 3 = 5.829Nm ( counterclockwise) But the book gives an answer...

Since q3=q4 and they are opposite to each others they cancel out But as soon as I try to find the electric field of one of the charges, I need the radius which is not given. By isolating the electric field for radius E=(kq)/r^2 I now have two unknowns

Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point...

How can we detect electrical effect of a static point charge at all? I think of a point charge like a sea urchin. With field lines going outwards in all directions (for +ve). So the vector pointing at me directly should be canceled perfectly by the vector going away from me. And so each line...