Electromagnetism - Infinite plane of charge & Tension

In summary, the concept of an infinite plane of charge in electromagnetism involves understanding the electric field produced by a uniformly charged plane, which is constant and directed perpendicular to the plane. The tension in this context refers to the forces experienced by charges in the field, influencing their motion and interactions. This scenario is vital in exploring electric fields, forces, and related concepts in physics, illustrating how charged materials can affect their surroundings.
  • #1
thejuanestevez
4
0
TL;DR Summary: Ping-pong ball hanging static from infinite plane of charge and a string

Really struggling with this question. I'm not sure if I have set up the free body diagram correctly and don't know how to set up the x and y components

Screenshot 2024-07-03 210524.png
setup.png
 
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  • #2
You setup looks fine. Now solve the system of equations.

There are perhaps ways of setting up the problem that make the solution easier, but we can discuss those once you have solved it.
 
  • #3
I agree with @Orodruin that your diagrams are correct. Nicely drawn!

However, your two force equations are not correct. Check these.
 
  • #4
TSny said:
I agree with @Orodruin that your diagrams are correct. Nicely drawn!

However, your two force equations are not correct. Check these.
Would this be correct:
Fx: T cos(10) = Fe cos(60)
Fy: T sin(10) = Fg + Fe sin(60)
 
  • #5
thejuanestevez said:
Would this be correct:
Fx: T cos(10) = Fe cos(60)
Fy: T sin(10) = Fg + Fe sin(60)
The first equation looks good. The second equation has a sign error.
 
  • #6
TSny said:
The first equation looks good. The second equation has a sign error.
Is it T sin(10) = Fe sin(60) - Fg ?
 
  • #7
thejuanestevez said:
Is it T sin(10) = Fe sin(60) - Fg ?
No. What is your reasoning behind setting up the two equations?
 
  • #8
TSny said:
No. What is your reasoning behind setting up the two equations?
I need to find Fe so that I can use it to find the charge of the of the ping pong ball. Fe is the force pushing the ball away, Fg and T are holding it static. So that should mean that T + Fg = Fe?
 
  • #9
thejuanestevez said:
I need to find Fe so that I can use it to find the charge of the of the ping pong ball. Fe is the force pushing the ball away, Fg and T are holding it static. So that should mean that T + Fg = Fe?
You are working with vectors. For static equilibrium, the net force must equal zero. So, the vector sum of the forces must equal zero. This means that the x-components of all the forces must add to zero and the y-components of the forces must add to zero:

##T_x + Fe_x + Fg_x= 0##
##T_y + Fe_y + Fg_y = 0##

You just need to fill in the correct expressions for each of the terms being careful with signs.
 
  • #10
Let me just add that splitting into components is not the way I would handle this particular problem. Even if I chose that route I would have chosen different directions to study the components in.
 

FAQ: Electromagnetism - Infinite plane of charge & Tension

What is an infinite plane of charge?

An infinite plane of charge is a theoretical concept in electromagnetism where a charged surface extends infinitely in two dimensions. This model simplifies the analysis of electric fields and potentials generated by a uniformly charged surface, allowing for easier calculations of electric fields at various points in space.

How do you calculate the electric field due to an infinite plane of charge?

The electric field (E) due to an infinite plane of charge with surface charge density (σ) is given by the formula E = σ / (2ε₀), where ε₀ is the permittivity of free space. The electric field is uniform and directed away from the plane if the charge is positive, and toward the plane if the charge is negative.

What is the relationship between electric field and tension in a charged system?

The tension in a charged system, such as a charged string or wire, can be influenced by the electric field. When a charged object is placed in an electric field, it experiences a force given by F = qE, where q is the charge and E is the electric field. This force can create tension in the medium if the charged object is constrained, leading to a relationship between the electric field and the tension experienced by the object.

How does the infinite plane of charge affect nearby charged objects?

Nearby charged objects will experience a force due to the electric field created by the infinite plane of charge. The uniform electric field will exert a force on the charges, causing them to accelerate in the direction of the field. The effect is independent of the distance from the plane, as the electric field produced by an infinite plane is constant and does not diminish with distance.

What assumptions are made when using the infinite plane of charge model?

When using the infinite plane of charge model, several assumptions are made: the plane is assumed to be uniformly charged, the effects of edge effects are neglected (since the plane is considered infinite), and the medium surrounding the plane is assumed to be vacuum or air, with a constant permittivity. These assumptions simplify the calculations but may not hold true in real-world scenarios where finite sizes and varying charge distributions exist.

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