Maxwell related equations converted from MKSA units to Gaussian units

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SUMMARY

The discussion focuses on converting Maxwell's equations from MKSA units to Gaussian units. The conversion requires multiplying the electric field (E) by \( \frac{1}{\sqrt{4\pi \epsilon_0}} \) and the charge density (p) by \( \sqrt{4\pi \epsilon_0} \), resulting in the equation \( E = p \cdot 4\pi \) in Gaussian units. The user seeks assistance in converting the equations involving vector fields and scalar potentials, specifically \( B = \nabla \times A \) and \( E = -\nabla T - \frac{1}{c} \frac{dA}{dt} \), back to MKSA units. References to resources for Maxwell's equations in both unit systems are provided for further clarity.

PREREQUISITES
  • Understanding of Maxwell's equations in both MKSA and Gaussian units.
  • Familiarity with vector calculus, specifically divergence and curl operations.
  • Knowledge of electromagnetic theory, particularly charge density and electric fields.
  • Basic understanding of unit conversion principles in physics.
NEXT STEPS
  • Study the conversion process of electromagnetic equations between MKSA and Gaussian units.
  • Learn about vector calculus operations such as divergence and curl in the context of electromagnetism.
  • Explore the implications of charge density in different unit systems, focusing on Gaussian units.
  • Review comprehensive resources on Maxwell's equations, such as those available at Wolfram ScienceWorld.
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism who need to understand unit conversions between MKSA and Gaussian systems.

Ed Quanta
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So here is an example of what I am trying to do.

We know that div of an E field=p/eo

where p=charge density and eo=the permittivity of free space. This equation is expressed in MKSA units. In order to convert this into Gaussian units, we must multiply E by 1/sqare root of 4*pi*eo, and multiply p by square root of 4*pi*eo.

Thus we are left with E= p*4*pi in Gaussian units

Now where A is a vector field and T is a potential scalar, I know that B=curl of A

and E=-gradient of T -1/c*dA/dt in the Gaussian unitss. I have to then convert this into MKSA. I am not sure what to do here because unlike the example which I dealt with above, I do not know how to convert both sides of the equation accordingly. Help anyone?
 
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This might help.
http://electron6.phys.utk.edu/phys594/Tools/e&m/summary/maxwell/maxwell.html
( http://electron6.phys.utk.edu/phys594/ for the main page)

I once tried to come up with a scheme to write the equations in a way that easily showed the conversion.

For example, I wrote [itex]\nabla\cdot E= \left[ \frac{1}{4\pi\epsilon_0}\right]4\pi \rho[/itex]. However, I never had the time to check that the whole scheme applied to all of electromagnetism was consistent.
 
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