What Are the Limits for Calculating the Radial Electric Field Potential?

In summary, to find the potential of a radial electric field near a charge 'q', we use the equation ΔV = -∫E dr, with the charge being constant. The limits for integration are from ∞ to r2, with V(∞)=0.
  • #1
chris_avfc
85
0

Homework Statement



Radial component of an electric field near charge 'q'.

E = (1 / 4∏ε) * (q/r^2)

Need to find the potential of this which is done through integrating this and taking the negative answer, i.e.

ΔV = -∫E dr

This is to be along a radial path towards the charge, starting from infinity to r2.


The Attempt at a Solution



So I have

ΔV = - (q/4∏ε) ∫1/r^2 dr

As the charge is constant.
Just unsure on the limits, I'm guessing its ∞ and r2, would that be right?
 
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  • #2
[tex]\Delta V=V(r)-V(\infty)=-\frac{q}{4\pi \epsilon _0}\int_{\infty}^r{\frac{1}{r^2}dr}[/tex],

with V(∞)=0


ehild
 
  • #3
ehild said:
[tex]\Delta V=V(r)-V(\infty)=-\frac{q}{4\pi \epsilon _0}\int_{\infty}^r{\frac{1}{r^2}dr}[/tex],

with V(∞)=0


ehild

Awesome, cheers mate. I had my limits the wrong way around.
 

1. What is a radial electric field?

A radial electric field is a type of electric field that extends outward or inward from a central point in a circular or spherical pattern. It is perpendicular to the surface of the circle or sphere at any given point.

2. How is a radial electric field created?

A radial electric field is created by a difference in electric potential between two points. This potential difference causes electric charges to move in a circular or spherical pattern, creating the radial electric field.

3. What is the significance of a radial electric field?

Radial electric fields play an important role in various physical phenomena, such as the movement of charged particles in a circular motion, the formation of electrically charged clouds in thunderstorms, and the behavior of plasma in nuclear fusion reactions.

4. How is a radial electric field measured?

The strength of a radial electric field can be measured using an electric field meter or by calculating the potential difference between two points in the field. The units for measuring electric field strength are volts per meter (V/m).

5. How can a radial electric field be controlled or manipulated?

Radial electric fields can be controlled or manipulated using various methods, such as applying an external electric field or changing the shape or size of the source of the field. This can be useful in applications such as particle accelerators and plasma confinement in fusion reactors.

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