Taking the vector E out of the Electric potential equation

[casanova2528]

the Electric field depends on the distance between the electric source and the point of measurement. Why can you take E out of the integral V = E dot dr? After all, E can't be constant from infinity to r sub zero...right? Is the integral supposed to be an approximate value?

need some assistance.

 

[casanova2528]

oh, I get it now...it was for a uniform field. never mind.

 

[astrokreng]

I would like to clarify that the electric potential equation is not V = E dot dr, but rather V = - ∫ E dot dr. The negative sign indicates that the integral is taken in the direction opposite to the electric field.

Now, to address your question, the reason why we can take E out of the integral is because the electric field is a conservative vector field. This means that the work done by the electric field in moving a charge from one point to another is independent of the path taken and only depends on the initial and final positions. In other words, the electric field remains constant along any path connecting the two points.

In the case of the electric potential equation, we are integrating the electric field over a specific path (dr) to calculate the potential difference between two points. Since the electric field remains constant along this path, we can take it out of the integral.

As for your concern about E being constant from infinity to r sub zero, it is important to note that the electric field is not constant in space. It varies with distance according to the inverse square law, where it decreases as the distance from the source increases. However, for a specific path, the electric field remains constant and that is why we can take it out of the integral.

The integral is not an approximate value, but rather a mathematical representation of the work done by the electric field in moving a charge from one point to another. It is a fundamental concept in electromagnetism and is used to calculate various properties of electric fields and potential. I hope this explanation helps clarify your doubts.