Line Definition and 1000 Threads

Homework Statement There are 4 wires with diameter d arranged in a way such that they form a square shape, with the wires on the corners. The horizontal distance is kD while the vertical distance is D. Prove that the inductance per meter of each conductor is 1/2 + 2ln { [2kd√(1 + k^2)] / d }...

Homework Statement Homework Equations flux = int(b (dot) ds) The Attempt at a Solution I just wanted clarification on finding ds. I understand why ds is in the positive yhat direction (just do rhr) but I don't understand where the dxdz come from. How do we find ds in general?

I didn't understand the following: The relationship between ##V_{CE} ## and ##I_C## is linear. In active region, even if the ##V_{CE}## increases, ##I_C## remains almost same for a given ##I_B##. So, how can the relation between the two can be linear? Can anyone tell me the utility of the...

Homework Statement A particle is moving along the x-axis. It is uniformly accelerated, in the sense that the acceleration measured in its instantaneous rest frame is always g, a constant. Find x and t as a function of the proper time ##\tau## assuming that the particle passes through ##x_0## at...

1. Homework Statement It is a part of the question in my homework and I extract this out just for the part i m confused(in the picture above) Homework Equations Moment couple=d*F [d is the difference in point of application (=sqrt41) or the perpendicular distance of the forces(=0) ?] The...

$\textsf{Write a complete solution.}\\$ $\textit{Let}$ $$v =\langle 1, 3, − 1 \rangle$$ $\textit{and }$ $$r_0 =\langle 1, 1, 1 \rangle$$ $\textit{and consider the line given by:}\\$ $$r = r_0+tv$$ $\textit{in vector form.}\\$ $\textit{Also, consider the plane given by}$ $$x+2y+2z+2 = 0$$...

Homework Statement Given an isolated system of 2 particles in space, we can express the motion of both particles as follows: $$m_1\ddot{\vec{x_1}}=-\frac\partial{\partial \vec{x_{1}}} V(\vec{x_1},\vec{x_2})\\ m_2\ddot{\vec{x_2}}=-\frac\partial{\partial \vec{x_2}} V(\vec{x_1},\vec{x_2}),$$ where...

Homework Statement What is the runtime complexity for the following (pseudo-code) algorithm?: Algorithm MyAlgorithm(A, n) Input: Array of integer containing n elements Output: Possibly modified Array A done ← true j ← 0 while j ≤ n - 2 do if A[j] >...

Homework Statement There is a finite line charge with length L = 1 meter and linear charge density λ = 1*10^-16 C/m. Point P is h = 70cm above the line charge and distance x from the right end of the line charge. The magnitude and direction of the electric field at point P must be found. The...

Homework Statement Draw this formula in line angle structure. CH3CH2OC(O)CH2CC(CH2)3CH(CN)CHO. Homework Equations None. The Attempt at a Solution I'm confused with the CC(CH2)3 part of the condensed formula. I knew I got it wrong the first time I drew it because I couldn't just tag three...

Let S be the minimal uncountable set. That is, for every m in S, there are countable many n s.t. n<m. Let L = { S x [0,1) } \ ##(a_0,0)## where ##a_0## is the smallest element of S (S is well ordered so this element exists). Order L be dictionary order, and then give L the order topology. Show...

I was just thinking of basic definitions of geometry and i came to this question, so how could i prove that only one straight line passes through two distinct points.

calculate the line integral for a vector field F= -xy⋅j over a circle which is c(t)=costi+sintj, so I used x=cost y=sint and ∫(0 to 2pi) -(sintcost)(cost)dt=(cos^3(2pi)-cos^3(o))/3=0 now here is the problem, if this enclosed line integral is zero then why is the vector field not conservative?

Homework Statement Homework EquationsThe Attempt at a Solution The answer is no as it is not dimensionally correct. Right?

Homework Statement It's stated in the notes that line fg is the flow line . Why is it so ? Homework EquationsThe Attempt at a Solution I think it's wrong . The flow line is defined as a line along which the water paticle travel from upstream to downstream in the permeable medium . However ...

I've been told that ##[0, 2 \pi )## is not homeomorphic to the unit circle in ##\mathbb{R}^2##. Why not? From intuition, it would seem that I could just bend the line segment to fit the shape of a circle.

Homework Statement Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. Determine a. The electric field produced by the charge distribution Q at points on the positive x-axis where x > a. b. A point charge q is then placed at x = a + r. Determine force on q due to Q...

Homework Statement Two identical thin rods of length L carry the same uniform line charge distribution (charge per unit length) of . If the two rods are collinear (aligned along the same line), with a distance of d between their nearest ends, calculate the Coulomb force (magnitude and...

The y-intercept of the line in the figure is 6. Find the slope of the line if the area of the shaded region is 72 square units. A line from quadrant 2 to quadrant 1 form a right triangle that is shaded. If the area of the shaded triangle is 72, then 6 • what = 72? The length on the x-axis...

Show that the slope of the line passing through the points (x, x^2) and (x + h, (x + h)^2) is 2x + h. Let m = slope The slope m is given to be 2x + h. 2x + h = [(x + h)^2 - x^2)/(x + h - x)] I must show that the right side = the left side. Correct?

Homework Statement I have a triangle with top sides of 5 mm (base is then 5*sqrt(2)). The top triangle has a line cut through it, at a height of 5/sqrt(2)/2. I want to compute the amplitude as function of position as a line sweeps into the triangle that is cut off. Requirement is A(0) = 0 and...

Hi I saw this 420 kV line and I am not able to figure out the meaning of the extra wire (marked with red arrow). My suggestion is that it is used to increase the tension in that particular cable, what do you think/know?

1. The problem statement, all variables, and given/known data Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1. Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4. Point F is the intersection of the line segments AE and...

Homework Statement What is the equation of a straight line passing through (1,2) and normal to ##~x^2=4y## Homework Equations Slopes of perpendicular lines: $$m_2=-\frac{1}{m_1}$$ The Attempt at a Solution $$x^2=4y~\rightarrow~m_1=y'=\frac{x}{2}$$ $$m_2=-\frac{2}{x}$$...

$\tiny{231.12.3.63}$ $\textsf{Determine the smallest distance between point $P(1,1,1)$}$ $\textsf{ and the line $L$ through the origin}$ $\textsf{ $L$ has the direction $\langle -4,-5,8 \rangle$}$ $\textit{ok I know the formula to use basically is}$ \begin{align*}\displaystyle...

The question: The line L1 has equation $$r = \left( \begin{array}{ccc}4 \\-1 \\0\\\end{array} \right) + t\left( \begin{array}{ccc}1 \\1 \\-1\\\end{array} \right) $$, and point A has coordinates (4, 8, -3). Find the coordinates of point B on L1, such that $$\overrightarrow{AB}$$ is...

$\tiny{231.12.3.65}$ $\textsf{Determine the smallest distance between point $P(1,1,1)$ and the line $L$ through the origin $L$ has the direction $\langle -4,-5,8 \rangle$}$ $\textit{ok I'm not real sure I understand this question so assume}\\$ $\textit{the line equation is derived first going...

Homework Statement A very thin, finite, and uniformly charged line of length 10 m carries a charge of 10 µC/m. Calculate the electric field intensity in a plane bisecting the line at ρ = 5 m. Homework EquationsThe Attempt at a Solution Not sure why I'm not getiting this but I've been at this...

Hi there, If I'm using the equation P_loss = P^2 * R / V^2 to calculation the power lost on a cable, where R = p(resistivity) * L(length) / A(cross sectional area), then how long is this power loss for exactly? Thanks, Sydney

How is it derived? ds^2 =-cdt^2+dx^2+dy^2+dz^2

I'm getting a bit confused by the specific notation in the question and am unsure what exactly it is asking here/how to proceed. Homework Statement Given a scalar function ##f## find (a) ##∫f \vec {dl}## and (b) ##∫fdl## along a straight line from ##(0, 0, 0)## to ##(1, 1, 0)##.Homework...

Homework Statement In a configuration having axial symmetry about the z axis, a line current I flows in the −z direction along the z axis. This current is returned at the radii a and b, where there are uniform surface current densities Kza and Kzb , respectively. The current density is zero in...

Homework Statement the line goes through (0, 3/2) and is orthogonal to a tangent line to the part of parabola y = x^2, x > 0 Homework EquationsThe Attempt at a Solution I have problems regarding finding the equation of tangent line to the part of parabola because the question not specifically...

Homework Statement find the shortest distance from (0,0) to the line passing A(2,3) and B(3,5) Homework Equations ## \frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} ## y-y1 = m (x-x1) m1 * m2 = -1 (m1 perpendicular to m2) The Attempt at a Solution line passing A and B points ## \frac{y-3}{5-3} ## =...

Hey! :o Let $g$ be a line with equation $g:ax+by+c=0$ in Hesse normal form. I want to show that the reflection across $g$ is described by \begin{equation*}\binom{x}{y}\mapsto \binom{x}{y}-2(ax+by+c)\binom{a}{b}\end{equation*} At the reflection across $g$ it holds the following for the image...

In http://vixra.org/abs/1406.0172, the five-dimensional Kaluza-Klein line element d˜s^2 is given by, Does this look correct? Thanks!

Hello all, I need your assistance with the following: Find the equation of the line that goes through the origin (0,0) if it is known that the sum of distances of the line from A(2,1) and B(1,4) is equal to \[\sqrt{8}\], and it is also known that the line is between the points. The formula I...

Homework Statement Two wires with the same intensity but with opposite directions. The magnetic field of the middle line between the two wires is: a) (X) b) (o) c) Parallel between the two wires d) Null e) Non of the above. Homework Equations N/A The Attempt at a Solution Knowing that they...

I work at a electric arc furnace. We measure a lot of items on our furnace and found that some weeks we preform well and other we do not (kwh/ton). With everything else being equal i believe that the utility's available short circuit current is affecting this. The utility feeds our substation...

Hey guys!. I need to use this method of minimization. The procedure to follow is explained here: http://es.tinypic.com/r/35mmtg0/9 However, I do not fully understand. What do I have to do? What I got from the paper is that I only have to minimize the equation 15.7.16, by using bisection. With...

1. Homework Statement Hello all. It is not a homework actually. I just didn't know at which forum I should post. I am working on a MATLAB code solving the finite wing properties iteratively by using the Anderson's Numerical Lifting Line Method. However, I got some wrong results. The...

I have an expression for a "line- to sphere intersection" that works: a = 1 + Ax^2 + Ay^2 b = 2*(-zs + Ax*(Bx-xs) + Ay*(By-ys)) c = zs^2 + (Bx-xs)^2 + (By - ys)^2 - R^2 This is part of a code in Matlab, and works fine. It is derived from substituting (x=Ax*z+Bx, y=Ay*z+By) into...

I have a single machine connected to an infinite bus with the following parameters: - Sending end power = 3.75MW - RL=5.18 ohms - XL=130 ohms - VS (Generator bus)=161kV - VR (Infinite bus)=161kV - Sending end voltage angle (delta) = 0.01877 (Angle which allows 3.75MW to be transferred)...

Homework Statement Consider a straight line segment of 3L and with a linear charge density λ. Determine the electric field, E, of at point P, which is a point within the segment and along the axis. (figure attached) Homework Equations dE=kdQ/r^2 The Attempt at a Solution I attempted solving...

What is the hyper-cylindrical line element?

Show that the slope of the line passing through the two points (x, x^2) and (x + h, (x + h)^2) is 2x + h. Let me see if I can solve this baby on my own. Let m = slope = 2x + h m = [(x + h)^2 - x^2]/[(x + h) - x] If I simplify the right side, it should give me m, right? At the very end, I...

Hi, I know this might be a bit dum but I'm currently stuck with this integral. In this link: http://www.pci.tu-bs.de/aggericke/PC4e/Kap_III/Linienbreite.htm I know he's doing the right thing, but I really don't understand the integral of a(omega). How come it is E(1/(i(ω-ω0) -γ) -...

The set of real numbers satisfying the given inequality is one or more intervals on the number line. Show each interval on the number line. 1. | x | < 2 Solution: -2 < x < 2 This can be written as (-2, 2). ----(-2-----0----2)---- Correct? 2. | x | > 0 Solution: The point x lies to the...

Hiya again, I am trying to solve this problem, I thought I got somewhere, but kinda stuck. The graph of y^2=x^3 is called a semicubical parabola. Determine the constant b so that the line y = -(1/3)x+b meets this graph orthogonally. I found the derivative of the curve by using implicit...

Homework Statement Here are the three problems that i couldn't solve from the book Calculus volume 2 by apostol 10.9 Exercise 2. Find the amount of work done by the force f(x,y)=(x^2-y^2)i+2xyj in moving a particle (in a counter clockwise direction) once around the square bounded by the...