Point charges in a regular hexagon

AI Thread Summary
The correct formula for the interaction of point charges in a regular hexagon is (2×sqrt3×k×q^2)/a^2. There is confusion regarding the definitions of 'a' as the hexagon's side length and 'R' as the distance from an outer charge to the center. The calculation for 'R' as (sqrt3 × a)/2 is incorrect. Considering the x and y components of the forces on the center charge simplifies the problem using symmetry. Clarification on these points is essential for accurate problem-solving.
rbh
Messages
9
Reaction score
1
Homework Statement
Regular hexagon with side length a, has q,q,q,q,-q,-q point charges in vertices. What force would point charge q expierence if it was put in a hexagon center?
Relevant Equations
F=(kq^2)/R^2
R=(sqrt3 × a)/2
The answer should be (2×sqrt3×k×q^2)/a^2. What did I do wrong?
 

Attachments

  • 20210328_135637.jpg
    20210328_135637.jpg
    110.4 KB · Views: 185
Physics news on Phys.org
I can't follow your working but...

Is 'a' the hexagon's side-length? Is 'R' the distance from an outer charge to the centre? If so, 'R=(sqrt3 × a)/2' is wrong!

Also, have you thought about the x and y components of each of the 6 forces on the centre charge? Then, using symmetry, the solution becomes very simple.

Edit - typo' corrected.
 
Last edited:
Steve4Physics said:
I can't follow your working but...

Is 'a' the hexagon's side-length? Is 'R' the distance from an outer charge to the centre? If so, 'R=(sqrt3 × a)/2' is wrong!

Also, have you thought about the x and y components of each of the 6 forces on the centre charge? Then, using symmetry, the solution becomes very simple.

Edit - typo' corrected.
Oh yeah, I mixed it up with inscribed circle radius, thanks.
 
Thread 'Minimum mass of a block'
Here we know that if block B is going to move up or just be at the verge of moving up ##Mg \sin \theta ## will act downwards and maximum static friction will act downwards ## \mu Mg \cos \theta ## Now what im confused by is how will we know " how quickly" block B reaches its maximum static friction value without any numbers, the suggested solution says that when block A is at its maximum extension, then block B will start to move up but with a certain set of values couldn't block A reach...
TL;DR Summary: Find Electric field due to charges between 2 parallel infinite planes using Gauss law at any point Here's the diagram. We have a uniform p (rho) density of charges between 2 infinite planes in the cartesian coordinates system. I used a cube of thickness a that spans from z=-a/2 to z=a/2 as a Gaussian surface, each side of the cube has area A. I know that the field depends only on z since there is translational invariance in x and y directions because the planes are...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Back
Top