A probe at , in spherical coordinates reads the physical (unit-vector) components of…

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

Conditions of Validity, Ch Gradient, divergence and curl without coordinates, and with any coordinates

Problem

A probe at

r=0.20\ \mathrm{m}

\theta=\pi/2

in spherical coordinates

(r,\theta,\phi)

reads the physical (unit-vector) components of a magnetic field as

B_{\hat r}=0.30\ \mathrm{T}

B_{\hat\theta}=0.10\ \mathrm{T}

B_{\hat\phi}=0.05\ \mathrm{T}

. ((a)) Find the coordinate (contravariant) components

B^r

B^\theta

B^\phi

at this point. ((b)) Give the units of each of the three coordinate components and explain why they differ from tesla.

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