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Relationship between electric field intensity and potential 
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#1
Jun2809, 03:52 AM

P: 102

I find that there are two ways in which the relationship between electric field intensity and potential are expressed as mentioned hereunder:
(A) E =  dV / dx (V = potential and x is the direction along which V varies) (B) E =  Delta V / Delta x My understanding of the application of (A) and (B) is as follows: (A) is the general case where the variation of V with x could be linear or nonlinear, i.e. E could be constant or variable along the x direction. E represents the limiting value of an incremental value of V divided by an incremental value of x (at a given value of x) as the increment in x is made infinitesimally small. Thus E is the gradient of the V versus x graph at any given value of x. (B) is a specific case of (A) when V varies linearly with x, when E is constant along the x direction. In this case the value of E would be the same irrespective of the values chosen for Delta V or Delta x. I would appreciate if the above understanding could be commented upon / ratified. Thanks. 


#3
Jun2809, 10:57 PM

P: 102

I am sorry if I have offended you in any way by my query. I genuinely request for a confirmation that my understanding is correct. Kindly advise. Thanks.



#4
Jun2809, 11:07 PM

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P: 5,197

Relationship between electric field intensity and potential
The only thing I would add to your post is that the most general statement of the relationship between the electric field and the electric potential is: [tex]\mathbf{E}=\nabla V[/tex] The other two equations are merely special cases of it, the second being common in introductory physics when students are not expected to have a grasp of vector calculus (or perhaps calculus of any kind) 


#5
Jun2809, 11:32 PM

P: 77

Your analysis of things is correct, kihr.



#6
Jun2909, 03:56 AM

P: 102

Thanks very much. Looks like I had goofed up with my interpretation of the English language!



#7
Jun3009, 07:28 PM

P: 1,035

E = grad V  dA/dt + (u X B). A = magnetic vector potential, u = velocity, B = magnetic flux density. Also, V = integral {E*dl} along a path. Claude 


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