Consider a sheet of 2d graphene in the x-y plane. The 2d sheet of graphene i...

Consider a sheet of 2d graphene in the x-y plane. The 2d sheet of graphene i then sut into a ribbon in the x direction. The energy becomes quantizes in the y direction. calcualte the charge carrier energies E as a function of kx and ky.

Expert Solution

genius_generous answered 2 years ago

Consider walks in the X-Y plane where each step is R: (x, y)→(x+1, y) or U:...

Consider walks in the X-Y plane where each step is R: (x, y)→(x+1, y) or U: (x, y)→(x, y+a), with a a positive integer. There are five walks that contain a point on the line x + y = 2, namely: RR, RU1, U1R, U1U1, and U2. Let a_n denote the number of walks that contain a point on the line x + y = n (so a_2 = 5). Show that a_n = F_{2n}, where F_n are the Fibonacci numbers...

Given an infinite sheet of charge occupying the x-y plane such that the charge density is...

Given an infinite sheet of charge occupying the x-y plane such that the charge density is constant and uniform, find the electric field at any point on the z-axis by: A) Using the point charge formula for the electric field directly in cartesian coordinates. B) Using the point charge formula for the electric field directly in cylindrical coordinates. C) Using the point charge formula for potential in cylindrical coordinates and taking the gradient. DO NOT USE GAUSS'S LAW

I. Consider the condition (x == y). How is this handled if x and y are...

I. Consider the condition (x == y). How is this handled if x and y are primitive types? How is this handled if x and y are objects? II. For the program to get a name interactively a Scanner object must be instantiated. Write the Java statement to do this. III. Write a statement using a Scanner method to get the first name interactively. IV. Write a method to extract the initial (first letter) from the first name. V. Write...

Consider the following utility functions: (i) u(x,y) = x2y (ii) u(x,y) = max{x,y} (iii) u(x,y) =...

Consider the following utility functions: (i) u(x,y) = x2y (ii) u(x,y) = max{x,y} (iii) u(x,y) = √x + y (a) For each example, with prices px = 2 and py = 4 find the expenditure minimising bundle to achieve utility level of 10. (b) Verify, in each case, that if you use the expenditure minimizing amount as income and face the same prices, then the expenditure minimizing bundle will maximize your utility.

Consider a two-dimensional ideal flow in the x-y plane (with radial coordinate r2 = x2 +...

Consider a two-dimensional ideal flow in the x-y plane (with radial coordinate r2 = x2 + y2). Given the velocity potentials of 1) a uniform flow, 2) a source φ = (q/2π) ln r, and 3) a dipole φ = −d · r/(2πr2): a) Using the principle of superposition, construct a linear combination of the ingredients above that gives the flow past an infinite cylinder. [10 points] b) Sketch the streamlines of the flow everywhere in space. [10 points]

h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane...

h Consider a solid T enclosed by the paraboloid z = x^2 +y^2 and the plane z = 4 (the solid above the paraboloid and below the plane). Let M the (closed) surface representing the boundary surface of T. The surface M consists of two surfaces: the paraboloid M1 and the lid M2. Orient M by an outward normal. Let F=(z,2y,-2) Compute the integral using the Divergence theorem. Carry out the computation of the triple integral using the spherical coordinates.

1a.Find the equation of the tangent plane to the surface √ x + √y + √...

1a.Find the equation of the tangent plane to the surface √ x + √y + √ z = 4 at P(1, 1, 4). 1b.Let f be a function of x and y such that fx = 3x − 5y and fy = 2y − 5x, which of the following is always TRUE? a. (0, 0) is not a critical point of f. b. f has a local minimum at (0, 0) c. f has a local maximum at (0, 0)...

1. Consider placing two point charges on an x-y plane, the first charge, q1, at (x1,...

1. Consider placing two point charges on an x-y plane, the first charge, q1, at (x1, y1), and the second charge , q2, at (x2, y2). 2. Derive an expression for the electric potential and field at any arbitrary point (x, y) in terms of q1, q2, x1, x2, y1 and y2. 3. Choose some reasonable values for q1, q2, x1, x2, y1 and y2 and make a rough sketch of what you expect the electric potential/field to look like....

Create a hot and cold game in Matlab to find a point in an (X,Y) 2D...

Create a hot and cold game in Matlab to find a point in an (X,Y) 2D coordinate plane. The user answers two inputs: x=Input('x') y=Input('y'). THE INPUTS WILL ONLY BE INTEGERS FROM 0 TO 100. This means no negative numbers. You write the program so the computer plays the game. The computer must play the game (comparing distances only) and give the same point as the user inputs. To keep it simple the code will check distances until distance =...

Three charges lie on a x-y plane: q1 = +12.0 nC on the y-axis at y...

Three charges lie on a x-y plane: q1 = +12.0 nC on the y-axis at y = +0.400m; q2 = -9.00microC on the x=axis at x = 0; q3 = -5.00microC on the x-axis at x = +0.300m. A. Use the component method to determine the net force on q1 due to other charges (show magnitude and direction). B. Confirm answer of net force by using the geometrical (graphical) method to add the individual force vectors (not components). Choose a...

Question