Net Electrostatic Force of 4 Charges at a Regular Triangle Pyramid

[basanti]

Homework Statement

4 identical charges each equal to Q are placed at the 4 vertices of a regular triangular pyramid of each side equal to 'a'. Find the net electrostatic force on anyone charge.

Homework Equations

F = kQ^2/a^2

The Attempt at a Solution

find the force due to each of the charges, resolve it into x- and y- components and hence add them..but this way i could not get the correct answer.

 

[Sabastien]

A problem I used to have is visualizing how the forces would interact. Where I believe you are going wrong is you are trying to make a 3d problem a 2d problem. When dealing with an regular triangular pyramid you'll find that due to symmetry and your charges all being the same most components cancel out.

You should have three forces F1=F2=F3.

You should be using the interior angle, the angle that the edge makes with the base plane. ( most people forget that its a 3d shape and find the angle between the edges.

Hint: If you imagine the pyramid on your desk the combined forces on the top vertex should be pointing straight up out of your desk.

Hope this helps.

Sabastien

 

[Redbelly98]

Homework Statement

4 identical charges each equal to Q are placed at the 4 vertices of a regular triangular pyramid of each side equal to 'a'. Find the net electrostatic force on anyone charge.

Homework Equations

F = kQ^2/a^2

The Attempt at a Solution

find the force due to each of the charges, resolve it into x- and y- components and hence add them..but this way i could not get the correct answer.

Welcome to PF.

Can you show the work you did, so people can see how far you got or where you might have gone wrong? Just saying, basically, "I tried this approach but it didn't work" doesn't really give a good basis for others to provide help. (For all we know, your answer is correct and the "correct" answer is wrong. Or maybe your answer is pretty close to the correct answer, and a reasonable grader would actually give you full credit for your solution. Without seeing your work and your solution, we have no way to tell.)

 

[Sabastien]

Being new, I responded before reading the rules (which states that you must show your work before anyone can help), my apologies.

 

[rezeew]

I would approach this problem by first understanding the concept of net electrostatic force and how it is affected by the distance and magnitude of charges. I would also consider the geometry of the regular triangular pyramid and how it affects the distribution of charges.

To find the net electrostatic force on any one charge, I would start by calculating the force due to each of the four charges using Coulomb's law, F = kQ^2/a^2. This would give me the magnitude and direction of the force acting on each charge.

Next, I would use vector addition to find the net force on the charge. Since the charges are placed at the vertices of a regular triangular pyramid, the net force would be directed towards the center of the base of the pyramid. By resolving the forces into x- and y-components, I can add them together to find the net force acting on the charge.

It's important to note that the net electrostatic force on any one charge in this scenario would depend on the magnitude of the charges and the distance between them. Therefore, the net force may vary depending on the specific values of Q and a. I would also consider the electric field at the location of the charge, as it would also contribute to the net force acting on the charge.

In conclusion, the net electrostatic force on any one charge in a regular triangular pyramid can be calculated by considering the forces due to each charge and using vector addition to find the net force. It's important to consider the geometry and distribution of charges in order to accurately calculate the net force.

 

[DeeNos]

I would approach this problem by first considering the Coulomb's law, which states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Using this law, the net electrostatic force on any one charge can be calculated by taking into account the contributions from all the other charges.

In this case, we have four identical charges arranged at the vertices of a regular triangular pyramid. By symmetry, we can assume that the force on any one charge will be equal in magnitude but opposite in direction to the forces from the three other charges. By using vector addition, we can determine the net force on any one charge.

First, we can calculate the distance between the charges using basic trigonometry, since we know the side length of the pyramid. Then, using Coulomb's law, we can calculate the magnitude of the force between each pair of charges. Finally, by adding these forces vectorially, we can determine the net electrostatic force on any one charge.

It is important to note that the direction of the net force will depend on the arrangement of the charges and the orientation of the pyramid. This approach allows us to accurately determine the net electrostatic force on any one charge in a regular triangular pyramid arrangement.