Can Coulomb's Law be Simplified for Finding Electric Field at Corners?

[NotMrX]

Hello,

I was wondering if we had a square with side length a and charges q. What would be the electric field at a corner? I can work this out by breaking stuff into components but I wondered if there was an easier way using very basic linear algebra. What about a cube? In other words are there any tricks to make it easier rather than just break it into components, add them, and find the resultant?

 

[berkeman]

It's not clear from your problem statement where the charge is with respect to the square, but my guess is that there is not a simple trick available. Adding components is something you will do a lot.

 

[kyle8921]

Thank you for your question. Coulomb's Law is a fundamental law in electromagnetism that describes the relationship between the electric force between two charged particles and the distance between them. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law can be used to calculate the electric field at any point in space, including corners.

While there may not be a shortcut or simplified version of Coulomb's Law specifically for finding the electric field at corners, there are some techniques that can make the calculation easier. One approach is to use vector addition to break the electric field into components, as you mentioned. Another technique is to use symmetry to simplify the calculation. For example, in the case of a square or cube with equal charges at each corner, the electric field at the corner will be the same in magnitude and direction. This can greatly reduce the number of calculations needed.

Additionally, there are numerical methods such as using computer simulations or conducting experiments to determine the electric field at corners. These methods can provide more accurate results and may be easier to implement for more complex shapes.

In summary, while there may not be a shortcut or simplified version of Coulomb's Law specifically for finding the electric field at corners, there are techniques and methods that can make the calculation easier and more accurate. It is important to carefully consider the problem at hand and choose the most appropriate approach for finding the electric field at corners.