Relationship between electric field intensity and potential

In summary, the two equations that Doc Al. referred to are the general case and the specific case of the relationship between the electric field intensity and the potential. The most general statement of the relationship is: "E = -grad V - dA/dt + (u X B)." The 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).
  • #1
kihr
102
0
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 non-linear, 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.
 
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  • #2
Looks like you understand things to me.
 
  • #3
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
kihr said:
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.

I doubt very much that you offended Doc Al. My interpretation of his post was that he was merely stating in a very succinct way that your original post looked correct and didn't contain any obvious errors. If it did, I'm almost certain he would have pointed them out. Perhaps with the following edits the meaning (as I understood it) becomes clearer: "[It] [l]ooks like you understand things [just fine] to me."

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
Your analysis of things is correct, kihr.
 
  • #6
Thanks very much. Looks like I had goofed up with my interpretation of the English language!
 
  • #7
cepheid said:
I doubt very much that you offended Doc Al. My interpretation of his post was that he was merely stating in a very succinct way that your original post looked correct and didn't contain any obvious errors. If it did, I'm almost certain he would have pointed them out. Perhaps with the following edits the meaning (as I understood it) becomes clearer: "[It] [l]ooks like you understand things [just fine] to me."

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)

This is NOT the most general relation. This only holds in the special case for conservative E fields. The more general expression is:

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
 

What is the relationship between electric field intensity and potential?

The relationship between electric field intensity and potential is described by the equation E = -∇V, where E is the electric field intensity and V is the electric potential. This means that the electric field intensity is equal to the negative gradient of the electric potential.

How does changing the electric potential affect the electric field intensity?

Changing the electric potential will directly affect the electric field intensity. An increase in electric potential will result in a stronger electric field intensity, while a decrease in electric potential will result in a weaker electric field intensity. This is because the electric field intensity is directly proportional to the electric potential.

What is the unit of measurement for electric field intensity and electric potential?

The unit of measurement for electric field intensity is volts per meter (V/m), while the unit of measurement for electric potential is volts (V).

How does the direction of the electric field intensity relate to the direction of the electric potential?

The direction of the electric field intensity is always perpendicular to the equipotential lines, which represent points of equal electric potential. This means that the electric field lines and equipotential lines are always perpendicular to each other.

What is the significance of the relationship between electric field intensity and potential?

The relationship between electric field intensity and potential is crucial in understanding the behavior of electric fields and their effects on charged particles. It allows us to calculate the force experienced by a charged particle in an electric field and predict its motion. It also helps us understand the concept of potential energy and how it relates to the movement of charged particles in an electric field.

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