GREPhysics.NET: GR9277 #64

GR9277 #64

Problem

GREPhysics.NET Official Solution

\prob{64}
If an electric field is given in a certain region by $E_x=0,E_y=0,E_z=kz$ , where k is a nonzero constant, which of the following is true?

There is a time-varying magnetic field.
There is charge density in the region.
The electric field cannot be constant in time.
The electric field is impossible under any circumstances.
None of the above.

Electromagnetism $\Rightarrow$ }Gauss Law

Gauss Law gives $\nabla \cdot \vec{E} = \rho/\epsilon_0$ . Since the divergence of E in Cartesian coordinates is non-zero, there is a charge density in the region. QED

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Comments

r10101
2007-10-27 16:32:37

Why does a small region of vacuum near the surface of an infinite charged plate (with constant $\vec{E}$ = E $\hat{n}$ normal to the surface) not satisfy this question, making answer (E) correct?

panos85
2007-10-31 05:12:32

It says $E_z=kz$ , not $E_z=k\hat{z}$ . The electric field near the surface of a conductor is constant, while the field in this problem is not.

tonyhong
2008-10-25 01:54:24

this is a trap...

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sharpstones
2006-12-01 10:25:11

how could you possibly construct a charge density that would make such an E field?

mhas035
2007-04-04 23:58:56

Remember that it says that the field is only in a certain region. We just need the region to be small with a relatively large charged plane of constant charge density.

evanb
2008-06-24 11:56:52

How about a uniform-density infinite-plane slab. So, it would be thick and the region of interest would be from the middle of the slab to the edge of the slab.

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Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

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