Rectangular Definition and 477 Threads

How to identify type of wave-guide mode here, like its TE or TM TE01 , TE10, TM11, TE02, TE20 . .. I read number of half wavelengths in x direction is the m and number of half-wavelengths in y direction is n. . .but I can't figure-out how . . .can somebody please explain

Homework Statement What is the magnitude of the velocity at t=4.00s? I would like to see if my approach and answer is correct. Homework Equations Position: r = {-30cos(\frac{\pi}{10}t) i + 30sin(\frac{\pi}{10}t) j - (7t) k} ft The Attempt at a Solution I took the first...

Homework Statement Using ∫∫kdA = k(b-a)(d-c), where f is a constant function f(x,y) = k and R = [a,b]x[c,d], show that 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32, where R = [0,1/4]x[1/4,1/2]. Homework Equations ∫∫kdA = k(b-a)(d-c) 0 ≤ ∫∫sin∏xcos∏ydA ≤ 1/32 The Attempt at a Solution I tried to...

Homework Statement On the XY there lies a conducting wire-rectangle with sides parallel to the axis. The current is given and constant. What is the magnitude of the magnetic field along an axis parallel to the z axis, going through the intersection of the rectangle's diagonals?Homework...

Given a matrix differential equation (system of equations?) of the form: \textbf{X}^{\prime}(t) = \textbf{AX}(t) (where X is a complex matrix, t is real scalar and A is always a square and normal real matrix) I am able to find (e.g. here) that a general solution for square \textbf{X} is...

Homework Statement I'm wondering this for any object with moment of inertia I, but I'll ask this question for a rectangle for simplicity and I'm sure I can extend it to general objects. Say we have a rectangular object (with mass m, height h, and width L) that is attached to a wall by some...

Homework Statement How fast is the volume of a rectangular box changing when the length = 6 cm, width = 5 cm and depth = 4 cm and the length and height are increasing at a rate of 1 cm/s and width is decreasing at a rate of 2 cm/s. Homework Equations Volume of a rectangle = l*w*h The...

Homework Statement A decorative window has the form of a rectangle surmounted by a semicircle whose diameter is equal to the top of the rectangle. If the TOTAL perimeter of the window 16+pi, then what is the maximum area? A. 25.653 B. 32.148 C. 15.923 D. 38.047 E. 30.018 Correct...

Vector Question: 3 dimensions inside a rectangular soild?? Homework Statement Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid along its three edges. a. Calculate the magnitude of the equilibrant of these three forces. b. Determine the angle that the equilibrant...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...

A) A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the side with length b. Express your answer in terms of given...

Hello , What is the electric field inside a hollow rectangular conductor of length ( L ) ?

Hello physicsForum.. I am trying to make a 2d physics engine for my game all on my own but I am stuck in the very basic problem. My problem is this.. If there is a rectangular body (with negligible depth since i am working on 2d) is present in free space as in attached file and a force of...

Homework Statement In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction. Homework Equations ΔxΔp=h/4pi...

Is there a name for a transformation using the orthonormal base s_k(x)=\lceil \sin kx \rceil,\: c_k(x) = \lceil \cos kx \rceil \quad ? So basically a Fourier transform or Fourier series using periodic rectangles. What are the properties? Is there some kind of convolution theorem?

I would like to compute $$ \iint \limits_{x^2 + y^2 \le 3} \! x^2 + y^2 \, \mathrm{d} A $$ using rectangular coord's. First, I'll compute the iterated integral using polar coordinates so that I can check my work. Limits: $$ 0 \le \theta \le 2\pi \\ 0 \le r \le 3 $$ so $$ \iint \limits_{x^2 +...

The steady state temperature $u(x,y)$ in a rectangular plate $0\leq x\leq L$, $0\leq y\leq M$, is sought, under the condition that the edge $x = 0$ is maintained at zero degrees, $x = L$ is kept at $u(L,y) = y$ degrees, and the edges $y = 0$ and $y = M$ are insulated. The appropriate...

No matter how or what strategy I try, I can't get the optimum value for $x$ in the following equation: $$V=4x^3-60x^2+200x$$ Let V=Volume of a rectangular prism, so: $$V'=12x^2-60x+200$$ Set V'=0 to get turning point $$12x^2-60x+200=0$$ The answer given in my text is when $$ x=2.11...

Hello everybody, I am solving a 2D problem of thermal stresses in a rectangular plate in which temperature is changing only y direction. Plate has fixed displacement conditions. Could anyone help me to find out analytical solution of thermal stresses for my problem? Does anyone suggest me...

Hi there, I'm trying to create a sheet that produces a uniform magnetic field,using either rectangular or cylindrical neodymium magnets. I can't tell you much abut their strength, but they would be the common type purchased from a science/hobby shop. Dimensions for cylinder are 10mm dia x...

Homework Statement An equation is given in spherical coordinates. Express the equation in rectangular coordinates. r2cos2∅=z So first thing I did was used a half angle formula r2 (cos2∅-sin2∅=z Now, I'm stuck. The answer is x2-y2=z Guidance is appreciated (: Homework...

Hello all. I am trying to change: E = (1/r) ar To rectangular coordinate system. Where ar is a unit vector. So I know r = √(x^2 + y^2) i also think ar = ax+ay, where ax and ay are unit vectors along the x-axis and y-axis respectively. So that would give me: E = (1/√(x^2 + y^2)) (ax...

When white light passes through a rectangular prism, will dispersion occur? Will emerging light ray comes out as a single white light ray or as seven different colors?

Translate the rectangular equation to spherical and cylindrical equations. http://www.texify.com/img/%5CLARGE%5C%21x%5E2%2By%5E2%2B2y-3x%2Bz%5E2%3D25.gif

Homework Statement 1.21 Express in cylindrical components: (a) the vector from C(3, 2,−7) to D(−1, −4, 2); (b) a unit vector at D directed toward C; (c) a unit vector at D directed toward the origin. I just want to know (a). And the solution from the book is attached, too...

Express in the following form z = x + iy: q. ln(i) This question came up in an exam i had today.. don't think i answered it correctly though! i went for the euler relation: e^i*θ = cos(θ) + i*sin(θ) next i set θ = 1 and found the natural log of the equation twice ln(i) = ln(ln(cos(1) +...

Some Background I am working on a soccer robotics project called RoboCup (perhaps people here have heard of it), which revolves around building a fleet of autonomous soccer robots that play against each other (league website - http://small-size.informatik.uni-bremen.de/ ). The kicking...

Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...

The electric field in a cubical cavity of side length L with perfectly conducting walls is E_x = E_1 cos(n_1 x \pi/L) sin(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_y = E_2 sin(n_1 x \pi/L) cos(n_2 y \pi/L) sin(n_3 z \pi/L) sin(\omega t) E_z = E_3 sin(n_1 x \pi/L) sin(n_2 y \pi/L)...

Hello, I have a rectangular object with the following properties: Mass (m) = 1 units Moment Of Inertia (I) = 4.41 units initial velocity (v_{i}) = (5, 0) initial angular velocity (w_{i}) = 0 If the block collides with a solid rigid wall with distance vector r = (1.1, 1.4) from the...

Homework Statement Given a homogenous rectangular surface, sides of length a and b=4*a, with a circular hole in x=a and y=a/2, find the center of mass. Homework Equations R=1/M*Ʃmi*ri , M= total mass, r= position vector area of a circle = pi*r2 , r being the radius The...

Homework Statement A rectangular coil of 80 turns has an area of 0.01m^2. It rotates @ 3000rpm about one of its in plane axes, in a uniform magnetic field having B=1.5T. Calculate the rms voltage generated. Homework Equations 1 Tesla= 1 Weber/m^2. Change in flux of 1 Weber per second...

Homework Statement I'm trying to solve the vibrations of a rectangular membrane with a rectangular hole inside. Both the inner and outer edges are fixed. I know i have to use the wave equation, but how do i write the boundary conditions in orden to incluye the hole? Any ideas? F.Y.I. I...

Homework Statement Elimnate the parameter to find a rectangular equation of the curve. x=sin t, y= csc t Homework Equations I believe trignometric identities are relevant to this problem. cscx=1/sinx The Attempt at a Solution csc x =1/ sin x thus y=1/x Is this the answer...

Hey guys, this is just a conceptual question so i don't think the scheme applies? I've got a circuit with a potential difference, when I use the right hand rule to determine the direction of the magnetic field created by the wire of any side of the rectangle, do I point my thumb (direction of...

Homework Statement Connect a battery to a solenoid A cylindrical solenoid 40 cm long with a radius of 8 mm has 250 tightly-wound turns of wire uniformly distributed along its length (see the figure). Around the middle of the solenoid is a two-turn rectangular loop 3 cm by 2 cm made of...

Consider a toroidal structure with a rectangular cross-section. If the toroid is defined by the surfaces r = 1cm and r = 4cm and the planes z = 0 cm and z = 2 cm, and the surface current density on the surface defined by r = 4cm is given by -60az A/m. (a) Specify the current densities on...

Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...

Homework Statement A rectangular loop of wire with dimensions 2.32 by 7.91 and resistance 0.557 is being pulled to the right out of a region of uniform magnetic field. The magnetic field has magnitude 3.01 and is directed into the plane of the following figure . At the instant when the...

"Find the maximum value of a rectangular box that can be inscribed in an ellipsoid.." Homework Statement Find the maximum value of a rectangular box that can be inscribed in an ellipsoid x^2 /4 + y^2 /64 + z^2 /81 = 1 with sides parallel to the coordinate to the coordinate axes...

"Find the most economical dimensions of a closed rectangular box [. . .]" Homework Statement Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and...

Homework Statement A rectangular loop with dimensions 4.2 cm by 9.5 carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 5.60×10−5 T and direction away from you as you view the plane of the loop.Homework Equations...

Homework Statement A rectangular coil of 90 turns has dimensions of 22 x 65 cm and is located in a uniform 1 T magnetic field. In 1.7 s, the plane of the coil is rotated from a position where it makes an angle of 19° with the magnetic field to a position where it makes an angle of 64°...

I am currently trying to provide a mathematical model that describes the flow through a diverging square pipe. I am trying to simplyfy the navier stokes equations by usings assumptions but am unsure if my current progress is correct. The problem is as follows: Fluid enters a section of a...

Homework Statement Find the area between y= 1/(x2+1) and the x-axis, from x=0 to x=1 The Attempt at a Solution so when x=0, y=1 and when x=1, y=1/2 next i plot the points, so the intersection of the given equation is (0,1) and (1,1/2) Yh= Y-higher= 1/(x2+1) Yl= Y-lower= 0 the...

Homework Statement A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode. take width to be...

Homework Statement A circuit consists of 7 sections of wire. The figure looks like a rectangle of length 9cm and width 5cm with a circle of diameter 3 cm cutting right through the middle of one of the 9cm sides so that the two sides of the circle are in parallel. Each of the sections of wire...

http://en.wikipedia.org/wiki/Squared_square It is known that simple perfect squared squares exist, with the lowest one being of order 21. It is also known that no simple perfect cubed cube exists, for the smallest cube would, again, require cubes atop it that form another squared square...

I'm worried about the process of solving this problem, can anyone help me? We are to make a rectangular box, including the top, that has a volume of 144 cubic inches and for which the base is twice as wide as it is deep. The bottom, which must be strong, is made of a material that is three...

Hi, I am looking for a formula that calculates self inductance and capacitance of rectangular spiral coil, i came across many formulas for helical coil and circular spiral coil but couldn't find one for rectangular coil, any help is highly appreciated. Thanks