A survey point is located at spherical polar coordinates , ,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Vector calculus and field geometry · Vector calculus and field geometry

Mathematical Methods for Physics, Ch Curvilinear and orthogonal coordinates

Problem

A survey point is located at spherical polar coordinates r=4 mr = 4\,\mathrm{m}, θ=π/3 rad\theta = \pi/3\,\mathrm{rad}, ϕ=π/6 rad\phi = \pi/6\,\mathrm{rad}, with θ\theta measured from the +z+z axis and ϕ\phi from the +x+x axis. ((a)) Write the three scale factors hrh_r, hθh_\theta, hϕh_\phi at this point. ((b)) Find the magnitude of ∂r^/∂ϕ\partial\hat{\mathbf{r}}/\partial\phi at this point. ((c)) Using the scale factors, find the volume dV\mathrm{d}V of the small curvilinear cell swept out by changing the coordinates by dr=0.010 m\mathrm{d}r = 0.010\,\mathrm{m}, dθ=0.020 rad\mathrm{d}\theta = 0.020\,\mathrm{rad}, dϕ=0.030 rad\mathrm{d}\phi = 0.030\,\mathrm{rad} from this point.

Browse the problem library