Electrostatic Potential of 4 charged spheres on corners of a square

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SUMMARY

The discussion centers on calculating the total electrostatic potential energy and kinetic energy of a system of four identical charged spheres positioned at the corners of a square with side length 2a. The total electrostatic potential energy is derived using the formula Utot=k(4√2q² + 2q²)/√2r. The kinetic energy gained by a sphere moving away from the other three is expressed as KE=1/2(4m)v², leading to the final speed of the sphere calculated as v=√(k*2q²/mr + q²/√2mr). The calculations confirm the relationships between potential and kinetic energy in electrostatic systems.

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  • Understanding of electrostatic potential energy and kinetic energy concepts
  • Familiarity with Coulomb's law and the constant k
  • Basic knowledge of algebra and square roots
  • Ability to manipulate equations involving multiple variables
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  • Explore the concept of potential energy in multi-particle systems
  • Learn about energy conservation principles in physics
  • Investigate the relationship between potential energy and kinetic energy in electrostatic contexts
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Students studying physics, particularly those focusing on electrostatics and energy conservation, as well as educators looking for examples of multi-body electrostatic interactions.

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Homework Statement


Four idential charged spheres are located at the corners of a square with side length 2a. The spheres are much smaller than the size of the square (r<<a) and each sphere has a mass m and carries the same charge -Q.

a) What is the total electrostatic potential energy of the combined 4-sphere system when arranged as described?
b) How much kinetic energy does a sphere gain by moving very far away from the other three?
c) What is the speed of a sphere moved very far away?


Homework Equations


Utot=kq1q2/r
KEf=Ui
KE=1/2mv^2


The Attempt at a Solution


For part a, I think i got the right answer: Utot=k(4root2q^2+2q^2)/root2r

b)KE=1/2(4m)v^2 and that's it because that's all we know

c) I used Ui=Kf
so k(4root2q^2+2q^2)/root2r=1/2(4m)v^2

and solve for v to get

v=squareroot(k*2q^2/mr+q^2/root2mr)
 
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im just wanting to know if I am right
 

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