Figure 1: Spherical coordinates Find the components of the acceleration vector a-r in spherical coordinates
5. The Cartesian components of the acceleration vector a are d2 Find the components of a in the spherical coordinates
Find the distance P1P2 vector between P1 (1, 2, 3) and P2 (-1, -2, 3) in Cartesian coordinates, cylindrical coordinates, AND spherical coordinates.
Calculate a) the components of (ar) in spherical polar coordinates, b) Ver , (Ver). Vxer , Vep, V x ee in spherical polar coordinates, c) the components of VX (a x r) in cylindrical coordinates (a =const.).
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
Find the tangential and normal components of acceleration of a particle with position vector r(t) = 4 sin ti + 4 cos tj + 3tk.
Traniate the vector و دما -4 to spherical coordinates. p = and y You must have p > 0. Traniate the vector 9 to cylindrical coordinates. r = 2 ܗ ܗ ܀ and • You must haver > 0.
Find the radial and angular components of acceleration for the motion TT r = 1 + cos e, = e-t at 0 2
(3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S
Find the gradient ∇φ of the following: a) φ = (r2/a2)e-r/a (using spherical coordinates) b) φ = 2√(x2+y2+z2) (using both cartesian and spherical coordinates, after converting)