Plot 3D graph of electric potential of a charged particle

In summary, to plot the electric potential ##V(r)## due to a positively charged particle located at the origin of an XY plane, you can use the formula ##V=\frac 1 {4πε_0} \frac q r## and plug it into a software like Matlab or online tools like WolframAlpha or Mathpix to generate a 3D plot. The formula can be derived from the electric potential equation for a point charge, and the plot will show the potential in relation to distance from the origin. The plot will not be labeled with axes, so it is important to note that the variable ##r## represents distance from the origin.
  • #1
AdrianMachin
40
2

Homework Statement


Plot the electric potential ##V(r)## due to a positively charged particle located at the origin of an XY plane.

Homework Equations


##V=\frac 1 {4πε_0} \frac q r##

The Attempt at a Solution


I'm unfamiliar with 3D coordinates at this time, but I like to know how can I plot it using a computer program like Matlab or online tools like WolframAlpha or Mathpix. I'm looking for the formula that I can plug into a software to see the 3D plot, plus an explanation for how to derive that formula. In the attachment, you can see the plot from my textbook (Fundamentals of Physics), but I don't why it's written ##V(r)## where no axes are named ##r##.
 

Attachments

  • plot.png
    plot.png
    30.1 KB · Views: 1,042
Physics news on Phys.org
  • #2
AdrianMachin said:

Homework Statement


Plot the electric potential ##V(r)## due to a positively charged particle located at the origin of an XY plane.

Homework Equations


##V=\frac 1 {4πε_0} \frac q r##

The Attempt at a Solution


I'm unfamiliar with 3D coordinates at this time, but I like to know how can I plot it using a computer program like Matlab or online tools like WolframAlpha or Mathpix. I'm looking for the formula that I can plug into a software to see the 3D plot, plus an explanation for how to derive that formula. In the attachment, you can see the plot from my textbook (Fundamentals of Physics), but I don't why it's written ##V(r)## where no axes are named ##r##.

I don't have access to Matlab or Mathematica (I use Maple instead), but a simple Google search on the keywords '3d plots in MATLAB turns up several articles on the topic.
 

Related to Plot 3D graph of electric potential of a charged particle

1. How do I plot a 3D graph of electric potential for a charged particle?

To plot a 3D graph of electric potential for a charged particle, you will need to have some knowledge of the mathematical equation for electric potential. Once you have this equation, you can use a graphing software or programming language such as MATLAB or Python to plot the graph. Alternatively, you can also use online graphing tools that allow you to input the equation and generate a 3D graph for you.

2. What factors affect the shape of the 3D graph of electric potential?

The shape of the 3D graph of electric potential is affected by the charge of the particle, the distance from the particle, and the distribution of other charges in the surrounding space. The shape can also be influenced by the presence of conductors or dielectric materials nearby.

3. How can I interpret a 3D graph of electric potential?

A 3D graph of electric potential shows the distribution of potential energy in space around a charged particle. The height of the graph at any point represents the potential energy at that point. The steeper the slope, the stronger the electric field is in that direction. Additionally, the distance between equipotential lines (lines with the same potential energy) can indicate the strength of the electric field.

4. Can I plot the 3D graph of electric potential for more than one charged particle?

Yes, you can plot the 3D graph of electric potential for multiple charged particles. In this case, the graph will show the combined potential energy distribution due to all the charged particles. However, the mathematical equation and programming may become more complex depending on the number and arrangement of the particles.

5. What are some real-life applications of plotting 3D graphs of electric potential?

Plotting 3D graphs of electric potential is commonly used in the field of electrostatics to study the behavior of charged particles and their interactions. It has practical applications in designing electronic circuits, analyzing the behavior of ions in mass spectrometry, and understanding the potential energy distribution in atoms and molecules.

Similar threads

Graphing electric potential for two positive charges
    • Introductory Physics Homework Help
Replies
16
Views
1K
Potential and Electric Field near a Charged CD Disk
    • Introductory Physics Homework Help
Replies
2
Views
392
Charge on a grounded conducting sphere in a uniform electric field, after ungrounding and movement
    • Introductory Physics Homework Help
Replies
1
Views
192
Several questions relating to work, electric potential energy, and potential difference
    • Introductory Physics Homework Help
Replies
22
Views
1K
Why Is the Electric Potential the Same for Inner and Outer Semi-Circles?
    • Introductory Physics Homework Help
Replies
7
Views
441
Ion moving through electric potential difference and magnetic field
    • Introductory Physics Homework Help
Replies
6
Views
202
Finding electric potential of an infinite line charge at z axis
    • Introductory Physics Homework Help
2
Replies
64
Views
2K
Kinetic and potential energy of a particle attracted by charged sphere
    • Introductory Physics Homework Help
Replies
6
Views
696
MIT OCW, 8.02 Electromagnetism: Potential for an Electric Dipole
    • Introductory Physics Homework Help
Replies
1
Views
927
Method of mirroring - metal plates
    • Introductory Physics Homework Help
Replies
11
Views
720

Hot Threads

Recent Insights

Back
Top