Gauss' Law

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Question statement

Gauss' Law is a powerful, general expression that links the arrangement of charges to the electric field strength, $\vec{E}$ . The mathematical formulation of the Law links the electric field flux through a closed surface, $\phi_{\rm electric}$ to the charge contained within that surface, $q$ .

When providing numerical answers you may express them using scientific notation. Express values to four significant figures and use the values of physical constants as provided in the course notes.

Give any introductory information the student needs.

			Name	Type	Generated Value

charge	decimal	dec("0")
chargee	decimal	dec("infinity")
eps0	decimal	dec("0.000000000008854")
flux	decimal	dec("0")
fluxnm	decimal	dec("0.000")
qe	decimal	dec("0")
nelec	integer	7

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
flux * eps0

JME function reference

Description

Charge contained within the Gaussian surface in C.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `decimal`

dec("0")

← Depends on:

eps0
flux

→ Used by:

chargee

"Charge" → "Charge" - Minimum accepted value
"Charge" → "Charge" - Maximum accepted value

Parts

Flux through the surface Gap-fill
1. Gap Flux through the surface Mathematical expression
  Add
Charge term Gap-fill
1. Gap Charge term Mathematical expression
  Add
Choice of Gaussian Surface Choose several from a list
Charge Gap-fill
1. Gap Charge Number entry
  Add
Number of electrons Gap-fill
1. Gap N Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

The flux through the surface expressed as an integral in terms of the electric field strength $\vec{E}$ (NUMBAS input Efield) and the elements of the surface, $d\vec{A}$ (NUMBAS input dA) is an integral over the closed surface, $S$ , expressed as

$\displaystyle \phi=\oint_S$ Flux through the surface

Your answer should be input as either a dot prodct using 'dot(a,b)' where a and b are the symbols for the vectors, or a cross product using 'cross(a,b)'.

Advice

This is partly a mathematical and partly a computational problem, but it centres upon the formulation of Gauss' Law as

$\displaystyle \phi_{\rm electric}=\oint_S \vec{E}.d\vec{A}={q\over\varepsilon}$ ,

where $\phi_{\rm electric}$ is the electric field flux through the closed Gaussian surface, $S$ , $\vec{E}$ is the electric field through $S$ , $d\vec{A}$ is an element of the surface area, $q$ is the total charge containined within $S$ and $\varepsilon$ is the permittivity.

To address the numerical part, we simply note that the arrangement of the charge is not relevant (Gauss' law applies whatever the arrangement of the charge within the closed surface) and so we can use

$\displaystyle |\phi_{\rm electric}|=\left|{q\over\varepsilon}\right|=\left|{e N_{\rm electron}\over\varepsilon}\right|$ ,

where $e=1.6\times10^{-19}$ C is the primitive charge.

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This question is used in the following exams:

All electromag by Jon Goss in EEE1001 & PHY1023.
TEST by Jon Goss in Jon's workspace.
E&M digital tutorial week 3 by Jon Goss in EEE1001 & PHY1023.

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Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Error in variable testing condition

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Generated value: `decimal`

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Gap-fill

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Gauss' Law

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: decimal

Parts

Gap-fill

Generated value: `decimal`