2-show that the representaton 14Cas6 oine, asingy -2 2 regular and lies on Yodius 2 about...
Eo z-h/2 The cylinder in the figure has radius a, height h and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P Poay with (a) Find the density of all polarization charge distributions that may exist within or on t he cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the origin. Briefly justify...
Question 1 2 έρ The cylinder in the figure has radius α, height and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P -Poa with Po > 0 (a) Find the density of all polarization charge distributions that may exist within or on the cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the...
Can someone answer this? Thanks! 2. Show that the language is not regular. 2. Show that the language is not regular.
Differential Geometry (4) Show that the helix α(t) = (2 cos(3t), 2sin(3t), 3t) lies on a circular cylinder, and find the arc-length of the helix. Determine β(s), the Reparametrized the helix by using the arc-length as the parameter.
Problem 2 A wire is bent into a quarter-circle of radius R. It is lies in Quadrant 2 of the xy plane with its center at the origin. The wire carries a charge density 0. Final answers not given (a) Derive an expression for E, at the origin (b) Derive an expression for E, at the origin. (c) Find the magnitude and direction of the net electric field at the origin
A charge of -2.2 micro-coulombs lies at the origin and another charge of +8.2 micro-coulombs lies at x = -11 cm, y = +7 cm. At a certain point, the total electric field from these two charges is zero. What is the y coordinate of this point in cm? Include a negative sign if negative. please show your work
please answer both questions 2. Find the volume of the solid that lies between the paraboloidand the plane -2x. Show your work by sketching the region. (8 pts.) 3. The region inside the curve r-2+sin 30 and outside the curve r 3-sin 30 consists of three same size pieces (draw the curves). Find the area of one of the pieces that lies in the first quadrant. Show your work. (8 pts.) 2. Find the volume of the solid that lies...
A charge of -2.2 micro-coulombs lies at the origin and another charge of +6.9 micro-coulombs lies at x = -15 cm, y = +6 cm. At a certain point, the total electric field from these two charges is zero. What is the y coordinate of this point in cm? Include a negative sign if negative. Please show all work & reply only if you're sure of the answer
please show the recurrence formula 1) Show that zo-0 is a regular singular point for the diferenta equation Zo = 0 is a regular singular point for the differential equation 15ェy" + (7 + 15r)y, +-y = 0, x>0. Use the method of Frobenius to obtain two linearly independent series solutions about zo Find the radii of convergence for these series. Form the general solution on (0, 0o). 0. 1) Show that zo-0 is a regular singular point for the...
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1, above the xy-plane, and below the plane z = 1 + x. Let S be the surface that encloses E. Note that S consists of three sides: S1 is given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2 + y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...