Problem 4 The parabolic cylindrical coordinates , , u) are related to the Cartesian coordinat es ...
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)...
RBH 11.28] Problem 5: A vector force field F is defined in Cartesian Coordinates by y's F Fo 'xy2 + a3 e*y/a2 j+ey/ak a Use Stokes' Theorem to calculate: F.dr L where L is the perimeter of the rectangle ABCD given by A = (0,1, 0), B = (1,1,0), C = (1,3, 0) and D = (0,3,0) RBH 11.28] Problem 5: A vector force field F is defined in Cartesian Coordinates by y's F Fo 'xy2 + a3 e*y/a2 j+ey/ak...
LE 4) (Ungraded) In Cartesian coordinates, the curl of a vector field Air) is defined as Use the definition of electric potential to find the potential difference between the origin and r = x + y + 27, V(r) - V(O) = - Ed. As the line integral is independent of path, choose whatever path you find to be con- vertient Taking V(0) = 0, what is V(r)? Finally, confirm that taking the gradient of the potential recovers our original...
solve problem 6 it is not a double integral, it is 1 integral In Convert to cylindrical coordinates ſyddy Set up the integral) 1b. Convert to spherical coordinates JJ Jy daddy (Set up the integral) 2. Une cylindrical coordinates to determine the volume of the solid in the 1" octant enclosed by the coordinate planes, the cylinder + 16 and the plane (Set up - do not solve) 3. Use spherical coordinates to determine the volume of the solid that...