Question

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 $F$

• A. $F=\frac{hc}{d^2}$
• B. $F=\frac{hc}{d^4}$
• C. $F=\frac{h{d}^2}{c}$
• D. $F=\frac{d^4}{hc}$

Answer 1

Answer: (B)

$F=\frac{newton}{m^2}$

$\frac{hc}{d^2}=$ joule-s.$\left(\frac{\text{metre}}{s.}\right)\frac{1}{{\left(\text{metre}\right)}^2}$

$=\frac{\text{joule}}{\text{metre}}=$newton

$\frac{hc}{d^4}=\left(\frac{hc}{d^2}\right)\frac{1}{d^2}=\frac{\text{newton}}{m^2}$. Hence $F=hc/d^4$

$\frac{hd}{c}=\frac{\text{joule.s}{\left(\text{metre}\right)}^2}{\left(\frac{\text{metre}}{s.}\right)}=$newton-metre${}^2{s}^2$

$\frac{d^4}{hc}=\frac{1}{\left(\frac{hc}{d^4}\right)}=\frac{m^2}{\text{newton}}$