Point Definition and 1000 Threads

Homework Statement The figure below shows a thin, vertical rod of length L with total charge Q. The indicated point P is a horizontal distance x from the one end of the rod. What is the electric field at point P. Express your answer in component notation in the two blanks below. L = 5.0 cm, Q...

Homework Statement Let ##(a,b)\subset \mathbb{R}## be a bounded open interval. Prove that if ##f:(a,b)\to\ \mathbb{R}## is strictly increasing at each point in ##(a,b)##, then ##f## is strictly increasing on ##(a,b)##. Homework Equations Let ##(a,b)\subset \mathbb{R}## be a bounded open...

Homework Statement "Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x-3 at the point B(3,3). (Picture of the graph: https://imgur.com/a/0wAnqcU) Homework Equations Here's a link: https://imgur.com/a/y71Z9GY The Attempt at a Solution Soo, I've...

Homework Statement Find the slope of ##y=x^2+4## at (-2,8) and the equation for this line. Homework EquationsThe Attempt at a Solution This problem is intended to give an intuition on how limits work and I think I get the general idea. If we want to find the rate of change (or slope) of some...

Knowing that a scalar quantity doesn't change under rotation of a coordinate system. Do we consider a point in a Cartesian coordinate system (i.e. A (4,5)) a scalar quantity? If yes, why do the components of point A change under rotation of the coordinate system? According to my understanding...

Homework Statement Homework Equations [/B]The Attempt at a Solution I got -1, but the answer says "6". Could you help me, please?

Can someone please show that calculation of gravitational potential energy at a point R+h from the centre of the Earth by choosing the centre of the Earth to be at zero potential. Here R is the radius of the Earth and h is not very small wrt to R

Flash point temperature of petrol is lesser than that of diesel at the same pressure. Does this mean, if I take petrol and diesel as liquids in separate containers and heat them, rapid vapourisation (rapid enough to sustain a combustion) of petrol occurs at a lower temperature(fire point) than...

Homework Statement A cylindrical conductor of length L and radius R, L » R, carries a charge Q. 1. Neglecting boundary effects; evaluate the potential difference between a point at distance r from the center of the cylinder, and the center. Assume r to be of the same order of magnitude as R but...

Okay, so I just found out about the Rayleigh distribution being the radial distribution of a point composed of normal distributed cartesian components. And this is because of the area element, right? But how then can the joint density of the cartesian component's distributions equal that of the...

Homework Statement Find potential of A and B in the given figure. (pardon poor quality, I only have a webcam) Homework Equations All related The Attempt at a Solution marking 1 to 4 from left to right. C1,C2,C3 are in series. C123=(2/3)C. which is in parallel with C4. C effective is 5C/3...

Homework Statement What is another form of point slope formula Homework Equations Y = mx+b The Attempt at a Solution Y - y2 = m(x - x2) I’m not sure I’m trying to find B but I don’t know how

Is there any difference between setting petrol on fire directly(by contacting it with burning stick) and heating petrol in a vessel, increasing its temperature above itself ignition temperature and making it burn spontaneously? What is the difference between flash point,fire point and self...

Hello, I'm having a visualisation problem. I have a point in R3 that I want to rotate about the ##y##-axis anticlockwise (assuming a right-handed cartesian coordinate system.) I know that the change to the point's ##x## and ##z## coordinates can be described as follows: $$z =...

A problem I solved asks this: There is a point charge of 3q at the origin and another charge of -2q at x = 5. At what value of x relative to the origin is the electric field equal to zero? So: E = E1 + E2 0 = E1 + E2 E1 = -E2 kQ1/x2 = -kQ2/(5-x)2 Solving for x, the point at which these...

Homework Statement Let ##K\neq\emptyset## be a compact set in ##\Bbb{R}## and let ##c\in\Bbb{R}##. Then ##\exists a\in K## such that ##\vert c-a\vert=\inf\{\vert c-x\vert : x\in K\}##. 2. Relevant results Any set ##K## is compact in ##\Bbb{R}## if and only if every sequence in ##K## has a...

How do you show that there can be only one tangent space at a given point of a manifold? Geometrically it's pretty obvious in 3 dimensions, as one notices that there can be only one tangent plane at a point. But how could we show that using equations?

Homework Statement Explain the following order of the boiling point (° C) HF (19.5)> HCl (-85.1) <HBr (-66.8) <HI (-35.4) b) Explain the following order of connection distance (pm): HF (92) <HCl (127) <HBr (141) <HI (161) Homework Equations xxx The Attempt at a Solution a) HF does hydrogen...

I see no correlation between a dimensionless point and a line although it appears that math has made one. I'm just a philosopher so it's quite possible that I've got it all wrong. It seems as though any location along a line is always the same location. If a location has no size then it can't...

Hello, I am encountering some confusion with the relation between the latent heat of vaporization and the temperature of a substance. I understand both the latent heat and the entropy change of vaporization are dependent on the temperature, assuming the pressure is held constant. However given...

Homework Statement Suppose we have a regular n-gon with identical charges at each vertex. What force would a charge ##Q## at the centre feel? What would the force on the charge ##Q## be if one of the charges at the vertices were removed? [/B]Homework Equations Principle of Superposition, the...

Good morning everyone. I have a question for the community. I am doing an optical project in which I need, as the title says, to concentrate white light in a very small point, with a diameter of the order of microns, so that I can pass light through a pinhole. I've been trying it with some lens...

https://ibb.co/guBuPd As the title indicates, I want to calculate the Probability of a stock price reaching a determined point, by considering the system as a random walk model, and after that, to compute the so called "maximal curves". I found the whole explanation in this article...

Homework Statement in title Homework Equations x=2cotθ y=2sin2θ dy/dx = 2sin3θcosθ y-y1=m(x-x1) point = (-2/√3,(3/2) The Attempt at a Solution Have been stuck for hours I solved for the dy/dx above, now I need to figure out how to get rid of the θ to get my equation in terms of x so I was...

Hi all, Can anyone help to solve this problem? Imagine a big plate suspended in the air through three threads with different length. we know length of each individual thread, and they are 120 degree apart from each other. How cam we calculate the tilt of the plate and direction of the tilt?

Dear All, I've been recently reading the very clear text of Burns and Glazer entitled Space Groups for Solid State Scientists in the context of my thesis which requires understanding of symmetries of crystals, more specifically symmetries of (approximate triply periodic minimal surfaces)...

My question is simple. Why do we need 9 different quantities, ie 1 normal stress and 2 shear stresses on 3 different planes, to define stress at a point? example: http://www.geosci.usyd.edu.au/users/prey/Teaching/Geol-3101/Strain/stress.html I think it should be enough to define the 3 stresses...

Homework Statement A factory is hiring ##m## employees. A number ##n > m## of candidates applied to the job. They need to answer an exam consisting of questions all of equal weight. A candidate is selected to the next step (the interview) if he/she achieves a minimum of ##c## points in the...

Homework Statement Homework Equations B=(μ0*I)/(2πr) The Attempt at a Solution B2 = (4*4*10-7)/(2*0.1) = 8 μT B1 = (3*4*10-7)/(2*0.1) = 6μT Could I know how to determine the directions ?

Homework Statement Refer the image. Homework Equations kq1q2/r^2 = F Potential energy = kq1q1/r The Attempt at a Solution Obviously since both charges are unequal in magnitude option a is incorrect. Calculating field at large distance r, E = kq1/r^2 - kq2/r^2 = kq2/r^2 Also potential energy...

I have a question regarding a theoretical analysis of Ultrasonic waves : The next picture represents a system of transducers sitting on fixed boards: Datum: * there are 4 transducers ( represented by blue color , indexed by letter ' T ' ) , each outputting Ultrasonic wave (represented by...

What is the GZK Cut Off point? I've seen an article stating that Prof. Silas Beane says a sort of 'lattice', an energy limit, which may suggest we are living in a matrix. But that can't be right? Can it? What actually causes it and why does it happen?

Homework Statement :[/B] A uniform wire of linear mass density λ having three sides each of length 2a is kept on a smooth horizontal surface. An impulse J is applied at one end as shown in the figure. P is the midpoint of AB. Now answer the following questions. 1) The angular velocity of system...

Homework Statement Express the electric field E due to a point charge q at the origin in cylindrical polar coordinates. Homework EquationsThe Attempt at a Solution Know that E = q / 4*pi*epsilon_0*r^2 in the r-direction, which is the answer in spherical coordinates. How we we swap to cylindrical?

Homework Statement Homework Equations Emec - PE = KE The Attempt at a Solution When particle starts at x = 4 KE = .5(.25)(225) = 28.125 Energy of system = 28.125 I don't have anything with position here so i am unsure how to find what position that the energy will be equal to the Emec and...

Homework Statement A radio speaker produces sound when a membrane called a diaphragm vibrates, as shown above. A person turns up the volume on the radio. Which of the following aspects of the motion of a point on the diaphragm must increase? a) the max. displacement only b) the average...

Homework Statement Homework EquationsThe Attempt at a Solution These AR type problems are mostly tricky and debatable . To me, A is correct and R is wrong . Although electron is approximated to be a point particle , but I think if R is true , then A will be wrong . I think c) is correct ...

Homework Statement Find the distance from point P (1,7,3) to the line (x,y,z) = (-2,1,4) + s(1,-3,4), s is a free variable Homework Equations projnQP = ( QP⋅n/(lengthQP)(lengthn) )(n) The Attempt at a Solution I'm not quite sure about how to find the normal (n) here, but if I make s=0, I'm...

Hi. I have read somewhere that cubic equations of state seem to have convergence issues when vapor pressure calculations are done near the critical point. Sadly, I have forgotten where I have have read it :( I would like to ask some knowledgeable people regarding this, or can people point me I...

Homework Statement A point charge q1=15.00μC is held fixed in space. From a horizontal distance of 8.00 cm , a small sphere with mass 4.00×10−3kg and charge q2=+2.00μC is fired toward the fixed charge with an initial speed of 40.0 m/s . Gravity can be neglected. What is the acceleration of the...

Hi, I want to know the relation between the point spread function (PSF) and the morphological index (Sharp, Sround, Ground). what does the PSF represent? and what is it's importance in the detection of astrophysical objects (quasars, galaxies)? Thanks

Hello Forum, I am clear on what the pressure at a point ##P## is on the wall of heigh of a dam at a certain depth ##d## below the water free surface: ## \rho g d+P_atm##. The deeper we go the higher the pressure. Now let's consider a different scenario: there is initially no water and water...

These days I've been reading in the internet about the Poisson Distribution because that was a concept I couldn't manage to understand completely when I studied it, so since then I've been always quite curious about Poisson processes, and how there are a lot of natural phenomena (mostly the...

Homework Statement Homework EquationsThe Attempt at a Solution My answer is d = |(a-b)x(p-b)|/|(b-a|). I first find out the area of the parallelogram produced by BA and BP and divide the area by length AB to get the height. Why am I wrong?

Homework Statement Four equivalent charges are placed at (0,0), (a,0), (0,a), and (a,a). What is the electric field at point B (a, a/2)? Homework EquationsThe Attempt at a Solution My attempt: Charges at (a,a) and (a,0) cancel each other out. E_{(0,a)}= \frac{Q(\hat{x}a...

Homework Statement Homework Equations ##E=\frac{kQ}{r^2}## 3. The Attempt at a Solution ##Q_{enclosed} = 0 ## , because there is no charge inside the conducting cylinder. E = 0 Can anyone check my answer please ?

Homework Statement The problem asks to find the direction of the magnetic field at point P, which is at the center of 2 separate semi-circle wires that form a circle. The current in each wire flows in the same direction (to the right). I attached a picture below. Homework EquationsThe Attempt...

Given an ABCD.EFGH cube whose its side length is 8 cm. The point P is within AB so that AP = 3PH. The distance between P to AC is ... A. 2\sqrt3 cm B. 3\sqrt3 cm C. 2\sqrt6 cm D. 3\sqrt6 cm E. 4\sqrt6 cm So AH is 8\sqrt2 cm and PH = 6\sqrt2. What do I do now? Is the triangle HPC a right triangle?

Homework Statement Homework Equations The Attempt at a Solution Can anyone check my answer please ?

Homework Statement When a workman strikes a steel pipeline with a hammer, he generates both longitudinal and transverse waves. The two types of reflected waves return 2.4 s apart. How far away is the reflection point? (For steel, vL = 6.2 km/s, vT = 3.2 km/s). Homework Equations Unknown...