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Electric field in a region with constant potential 
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#1
Mar2010, 10:44 PM

P: 5

1. The problem statement, all variables and given/known data
When the potential is constant throughout a given region of space, is the electric field in the region also zero? 2. Relevant equations in a parallel plate capacitor, electric filed =  delta V / delta d 3. The attempt at a solution It is difficult to understand how in a given region where the electric potential could be constant. That means at any given location, V=kq/r is the same everywhere and delta v equals zero. I can only relate this to a plate capacitor where the electric field is defined as  delta v / delta d. If delta v is zero, then E=0. Am I on the right track? 


#2
Mar2010, 11:44 PM

P: 393

[tex]E = \frac{dV}{dr}[/tex] this equation simplifies to the one you wrote if the rate of change of voltage with respect to displacement is a constant. So electric field equals the negative of the rate of change in voltage. If voltage is constant, meaning it has a rate of change of zero, electric field also is zero. 


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