Bringing 3 Charges from infinity into a triangle

In summary, to arrange three charges, Q, into an equilateral triangle, the work needed is (3kQ^2)/a. This includes bringing in each charge from infinity and accounting for the pair-wise interactions between the charges. This is derived from the equation U = (kqq)/L.
  • #1
lilpoopoo
6
0

Homework Statement



How much work is needed to arrange three charges, Q, into an equilateral triangle? The particles are initially infinitely far apart. Take 'a' to be the length of each side of the triangle.

Homework Equations



U = {(kqq)/L}

The Attempt at a Solution



I was under the assumption it takes no work to bring the first charge, Q1, from infinity since no other force is present.

To bring in charge #2 requires:

U = (kQ1Q2)/a = (kQ^2)/a

To bring in charge #3 requires a greater U since two charges are already present. I added the two pair-wise interactions of Q1 with Q3, and Q2 with Q3:

U = (kQ1Q3)/a + (kQ2Q3)/a = (2kQ^2)/a

Add both U's and get:

(3kQ^2)/a

------

Is this correct?
 
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  • #2
Yes, it is correct.

ehild
 

1. How do you bring 3 charges from infinity into a triangle?

To bring 3 charges from infinity into a triangle, you would need to use a process known as "charging by induction". This involves placing a positively charged object (known as a "source charge") near the triangle, which will then exert a force on the 3 charges and attract them towards the triangle. This process can be repeated multiple times to ensure that the 3 charges are evenly distributed within the triangle.

2. What is the purpose of bringing 3 charges from infinity into a triangle?

The purpose of bringing 3 charges from infinity into a triangle is to study the interactions and effects of these charges within a specific geometric shape. By bringing the charges into the triangle, we can observe the forces and potentials created by the charges and analyze the resulting electric field within the triangle.

3. What factors affect the strength of the electric field within the triangle?

The strength of the electric field within the triangle is affected by the magnitude and distance of the 3 charges within the triangle, as well as the shape and size of the triangle itself. Additionally, the presence of any other charges or conductive materials in the vicinity can also impact the strength of the electric field.

4. What are some applications of studying the electric field within a charged triangle?

Studying the electric field within a charged triangle can have various applications in fields such as physics, engineering, and chemistry. It can help us understand the behavior of charged particles and their interactions within different geometries, which can be applied to the design of electronic devices, chemical reactions, and even the structure of molecules.

5. Can the process of bringing 3 charges from infinity into a triangle be applied to other geometric shapes?

Yes, the process of bringing 3 charges from infinity into a triangle can be applied to other geometric shapes as well. The key concept is charging by induction, which can be used to evenly distribute charges within any given shape. This can be particularly useful in studying the electric field and its effects within complex structures and systems.

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