A question about units in equation: Dimensional analysis

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SUMMARY

The discussion centers on the dimensional analysis of the equation for electron mobility, which is expressed in units of m²/V·s. The user, GH, encountered discrepancies when substituting units and simplifying using MKSA (Meter-Kilogram-Second-Ampere) units. Participants emphasized the importance of reducing all terms to MKSA and highlighted the need to consider the charge of the electron in relation to voltage. The conversation underscores the necessity of understanding derived units versus fundamental units in dimensional analysis.

PREREQUISITES
  • Understanding of MKSA (Meter-Kilogram-Second-Ampere) units
  • Familiarity with dimensional analysis techniques
  • Knowledge of derived and fundamental units in physics
  • Basic concepts of electron charge and voltage relationships
NEXT STEPS
  • Study the principles of dimensional analysis in physics
  • Learn about the significance of derived units versus fundamental units
  • Explore the relationship between charge, voltage, and mobility in semiconductor physics
  • Review the MKSA system and its applications in electrical engineering
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Students and professionals in physics, electrical engineering, and anyone involved in the analysis of electrical properties of materials will benefit from this discussion.

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This question is about the matching the unites in an equation.

The equation for an electron mobility is given by m^2/V.S.
However substituting the units in the equation, doesn't yield the unit of mobility [m^2/V.S]. I have done the simplification using mks units and didn't come up to m^2/V.S. Have a look at the attached file, and help is appreciated.

Thanks
GH
 

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Welcome to PF.

Dimensional analysis is the truth. The equations may be wrong, or you may be confusing derived units with the fundamental MKSA system.

Try to reduce everything to MKSA. Avoid V, which is = M⋅L2⋅T−3⋅I−1

An electron has charge, where does that appear in the equation with voltage?
https://en.wikipedia.org/wiki/Dimensional_analysis
 

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