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121 lines
4.5 KiB
Python
121 lines
4.5 KiB
Python
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"""
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Title : Finding the value of magnitude of either the Casimir force, the surface area
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of one of the plates or distance between the plates provided that the other
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two parameters are given.
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Description : In quantum field theory, the Casimir effect is a physical force
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acting on the macroscopic boundaries of a confined space which arises from the
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quantum fluctuations of the field. It is a physical force exerted between separate
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objects, which is due to neither charge, gravity, nor the exchange of particles,
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but instead is due to resonance of all-pervasive energy fields in the intervening
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space between the objects. Since the strength of the force falls off rapidly with
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distance it is only measurable when the distance between the objects is extremely
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small. On a submicron scale, this force becomes so strong that it becomes the
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dominant force between uncharged conductors.
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Dutch physicist Hendrik B. G. Casimir first proposed the existence of the force,
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and he formulated an experiment to detect it in 1948 while participating in research
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at Philips Research Labs. The classic form of his experiment used a pair of uncharged
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parallel metal plates in a vacuum, and successfully demonstrated the force to within
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15% of the value he had predicted according to his theory.
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The Casimir force F for idealized, perfectly conducting plates of surface area
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A square meter and placed at a distance of a meter apart with vacuum between
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them is expressed as -
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F = - ((Reduced Planck Constant ℏ) * c * Pi^2 * A) / (240 * a^4)
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Here, the negative sign indicates the force is attractive in nature. For the ease
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of calculation, only the magnitude of the force is considered.
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Source :
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- https://en.wikipedia.org/wiki/Casimir_effect
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- https://www.cs.mcgill.ca/~rwest/wikispeedia/wpcd/wp/c/Casimir_effect.htm
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- Casimir, H. B. ; Polder, D. (1948) "The Influence of Retardation on the
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London-van der Waals Forces", Physical Review, vol. 73, Issue 4, pp. 360-372
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"""
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from __future__ import annotations
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from math import pi
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# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
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# Pi and the function
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REDUCED_PLANCK_CONSTANT = 1.054571817e-34 # unit of ℏ : J * s
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SPEED_OF_LIGHT = 3e8 # unit of c : m * s^-1
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def casimir_force(force: float, area: float, distance: float) -> dict[str, float]:
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"""
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Input Parameters
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----------------
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force -> Casimir Force : magnitude in Newtons
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area -> Surface area of each plate : magnitude in square meters
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distance -> Distance between two plates : distance in Meters
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Returns
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-------
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result : dict name, value pair of the parameter having Zero as it's value
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Returns the value of one of the parameters specified as 0, provided the values of
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other parameters are given.
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>>> casimir_force(force = 0, area = 4, distance = 0.03)
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{'force': 6.4248189174864216e-21}
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>>> casimir_force(force = 2635e-13, area = 0.0023, distance = 0)
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{'distance': 1.0323056015031114e-05}
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>>> casimir_force(force = 2737e-21, area = 0, distance = 0.0023746)
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{'area': 0.06688838837354052}
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>>> casimir_force(force = 3457e-12, area = 0, distance = 0)
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Traceback (most recent call last):
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...
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ValueError: One and only one argument must be 0
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>>> casimir_force(force = 3457e-12, area = 0, distance = -0.00344)
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Traceback (most recent call last):
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...
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ValueError: Distance can not be negative
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>>> casimir_force(force = -912e-12, area = 0, distance = 0.09374)
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Traceback (most recent call last):
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...
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ValueError: Magnitude of force can not be negative
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"""
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if (force, area, distance).count(0) != 1:
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raise ValueError("One and only one argument must be 0")
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if force < 0:
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raise ValueError("Magnitude of force can not be negative")
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if distance < 0:
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raise ValueError("Distance can not be negative")
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if area < 0:
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raise ValueError("Area can not be negative")
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if force == 0:
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force = (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
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240 * (distance) ** 4
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)
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return {"force": force}
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elif area == 0:
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area = (240 * force * (distance) ** 4) / (
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REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
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)
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return {"area": area}
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elif distance == 0:
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distance = (
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(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
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) ** (1 / 4)
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return {"distance": distance}
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raise ValueError("One and only one argument must be 0")
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# Run doctest
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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