Electrostatic Potential of 4 charged spheres on corners of a square

In summary, four identical charged spheres with mass m and charge -Q are arranged at the corners of a square with side length 2a. The total electrostatic potential energy of the system can be calculated using the equation Utot=k(4root2q^2+2q^2)/root2r. For part b, the kinetic energy gained by a sphere moving far away from the other three is given by KE=1/2(4m)v^2. And in part c, the speed of a sphere when moved very far away can be found by equating the initial potential energy to the final kinetic energy, which results in the equation v=squareroot(k*2q^2/mr+q^
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sweetdion
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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
 

Related to Electrostatic Potential of 4 charged spheres on corners of a square

What is the electrostatic potential of a system of four charged spheres placed at the corners of a square?

The electrostatic potential of a system of four charged spheres on the corners of a square is determined by the sum of the individual potential energies of each sphere. This can be calculated using Coulomb's law, which states that the potential energy between two charged objects is directly proportional to the product of their charges and inversely proportional to the distance between them.

How is the electrostatic potential affected by the distance between the charged spheres?

The electrostatic potential is inversely proportional to the distance between the charged spheres. This means that as the distance between the spheres increases, the electrostatic potential decreases. Conversely, as the distance between the spheres decreases, the electrostatic potential increases.

What is the impact of the magnitude of the charges on the electrostatic potential?

The electrostatic potential is directly proportional to the magnitude of the charges on the spheres. This means that as the charges increase, the electrostatic potential also increases. Therefore, if the charges on the spheres are doubled, the electrostatic potential will also double.

Can the electrostatic potential of the system be negative?

Yes, the electrostatic potential of the system can be negative. This occurs when the charges on the spheres are of opposite signs, causing the potential energies to cancel each other out. The overall electrostatic potential of the system is then determined by the difference between the potential energies of the individual spheres.

How does the arrangement of the charged spheres affect the electrostatic potential?

The arrangement of the charged spheres can have a significant impact on the electrostatic potential. In a system of four charged spheres on the corners of a square, the potential will be different depending on whether the spheres are arranged in a clockwise or counterclockwise direction. In other arrangements, such as a triangle or a line, the electrostatic potential will also vary.

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