In cylindrical coordinates (r, , z), a torus (a.k.a. the mathematical doughnut) has the equation
Change the coordinate system from cylindrical coordinates (r, , z) to torodial coordinates () where
Find the surface area of the torus.
In cylindrical coordinates (r, , z), a torus (a.k.a. the mathematical doughnut) has the equation Change the coordinate...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus. c) Use double integral to get the surface area of this torus. d) Let's say you have a circle on the xy-axis with the centre (a, a) and radius b as shown in the figure below, where a > b....
2014/B5 (a) Draw skecthes to illustrate R, 0 and z coordinate curves for the case of cylindrical polar coordinates (b) Show that the gradient of a scalar field, p, can be expressed in terms of curvilinear coordinates u1, u2 and us, of an orthogonal coordinate system as where h, Idr/dul. Hence obtain a formula for Vip in cylindrical polar coordinates. (c) Evaluate dp/ds, the rate of change of φ with distance, for the field φ-R, cost) at the point R...
1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the torus? b) Use double integral to get the volume of this torus c) Use double integral to get the surface area of this torus. 1. A torus has 2 parameters r and r that are related to the equation a) Based on the above equation, what is a and b for the...
1. (a) Using cylindrical coordinates, set up an integral to calculate the volume of the region inside the ellipsoid 4.r? + 4y + z2 = 1 and above the plane z = -1/2. We were unable to transcribe this image
Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point. (AI(24) (b) (5, -, 3) We were unable to transcribe this image
#3 3. Using the change of coordinate formulas" find the partial derivatives of x, y, and z with respect to the cylindrical coordinates r, 0, z. 4 Using change of coordinate for 3. Using the change of coordinate formulas" find the partial derivatives of x, y, and z with respect to the cylindrical coordinates r, 0, z. 4 Using change of coordinate for
Relativistic case: Starting from equation invert it to get . Restore factors of G and c. Get the expression for V(r), the "coordinate speed," for a particle falling from rest at . Take the Derivative with respect to r to find the location where the maximum coordinate speed occurs. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
A charge is glued on the cylindrical surface of a long circular cylinder of radius R. The cylinder is made of a linear dielectric material of dielectric constant . Find the electric field inside the cylinder and show that this field is uniform. If a small metal sphere of radius a (a<< R) gets into the center of the cylinder, find the total dipole moment of the setup by all charges: free charge, bound charge, and induced charge, given the...
Setup triple integrals of f(x,y,z) in sepherical coordinates for each of the regions below. The region to the left (-y direction) of and the right (+y direction) of that is not contained in the first or fourth octant. We were unable to transcribe this imageWe were unable to transcribe this image