Textbook says V=E/w but units don't match

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Discussion Overview

The discussion revolves around the formula for potential difference in the context of the Hall Effect, specifically the equation V=E/w, where E is the induced electric field and w is the width of the conductor. Participants are analyzing the dimensional consistency of this equation and questioning its validity based on unit analysis.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the textbook states V=E/w, but claims that the units for E appear to be inconsistent, suggesting E=volts*meter instead of the expected volts/meter.
  • The same participant performs dimensional analysis on the equation V=E/w and concludes that it leads to an incorrect unit for potential difference.
  • Another participant suggests that the formula might be a typo and proposes that it should be V=Ew instead.
  • Further replies confirm the suggestion of a typo without providing additional justification.
  • Participants inquire about the source of the formula, with one identifying the textbook as Halliday and Resneck Physics Volume 2 Edition 4, page 745.
  • There is a comment on the age of the textbook edition being referenced.

Areas of Agreement / Disagreement

There is no consensus on whether the formula V=E/w is correct or if it is indeed a typo. Some participants agree on the possibility of a typo, while others focus on the dimensional analysis without resolving the disagreement.

Contextual Notes

The discussion highlights potential limitations in the dimensional analysis presented, as well as the dependence on the definitions of the terms involved. The validity of the formula remains unresolved.

Who May Find This Useful

Students and educators interested in the Hall Effect, dimensional analysis, and the interpretation of physics textbooks may find this discussion relevant.

SherlockHolmie
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In my textbook, it is talking about the Hall Effect on a flat conductor with width w carrying a current i in a uniform magnetic field perpendicular to the plane of the strip. It says that this will create a potential difference of V=E/w where E is the induces electric field from the electrons moving to the right side of the material.

In normally, E=volts/meter, but here, we have E=volts*meter.

Doing deeper dimensional analysis based on V=E/w, we get kg*m^2/(s^3*(A)=(kgm/(s^3*A))/m=kg/(s^3*A) where A is current, which is false.

Why is this potential difference formula different?

Thanks
 
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SherlockHolmie said:
Why is this potential difference formula different?
Because it's a typo.
 
kuruman said:
Because it's a typo.
It should be V=Ew, right?
 
SherlockHolmie said:
It should be V=Ew, right?
Right.
 
What book? What page? Can you post a scan of the page?
 
nasu said:
What book? What page? Can you post a scan of the page?
Halliday and Resneck Physics Volume 2 Edition 4 page 745.
 

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Wow! 4th edition. That's an old one.
 

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