In a region of space an electrostatic field is described

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

Electricity, Magnetism and Electromagnetism, Ch Divergence, curl and the local form of the field laws

Problem

In a region of space an electrostatic field is described, in Cartesian components, by

\mathbf{E} = (400\,x)\,\hat{\mathbf{x}} - (100\,y)\,\hat{\mathbf{y}} - (200\,z)\,\hat{\mathbf{z}},

where

x

y

and

z

are measured in metres, the numerical coefficients are in

\mathrm{V\,m^{-2}}

and

\mathbf{E}

comes out in

\mathrm{V\,m^{-1}}

. The formula is valid throughout the region. ((a)) Compute

\nabla\cdot\mathbf{E}

at any point of the region. ((b)) Compute the three components of

\nabla\times\mathbf{E}

, and say whether a small paddle wheel placed anywhere in this field would spin.

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