An experiment shows that two perfectly neutral parallel metal plates separated by a small distance d attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, F, depends only on the Planck constant h, on the speed of light c, and on d. Which of the following has the best chance of being correct for F?
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a
F=hcd2
b
F=hcd4
c
F=hd2c
d
F=d4hc
answer is B.
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Detailed Solution
F= Newton m2hcd2= joule-sec metre sec1(metre)2 = joule metre = Newton hcd4=hcd21d2= Newton m2. Hence F=hc/d4hdc= Joule.sec (metre) 2 metre sec. = Newton-metre 2sec2d4hc=1hcd4=m2 Newton