A static charge distribution produces the potential V(x,y,z) = A x^2 y + B y z^3 + C x z

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential

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

Problem

A static charge distribution produces the potential

V(x,y,z) = A x^2 y + B y z^3 + C x z,

with

A = 4.0

V m

^{-3}

B = -3.0

V m

^{-4}

C = 5.0

V m

^{-2}

and

x

y

z

in metres. ((a)) Write the three components of

\mathbf{E} = -\nabla V

. ((b)) Compute all three components of

\nabla\times\mathbf{E}

, showing term by term how each one cancels. ((c)) Show that the same cancellation happens for any smooth

V

, naming the property of second derivatives you use. ((d)) State in one sentence what

\nabla\times\mathbf{E} = 0

says about the static electric field, and how it is related to the zero circulation of Chapter 3.

Browse the problem library