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A length -scale (l) depends on the permi...

A length -scale (l) depends on the permittivity `(epsilon)` of a dielectric material, Boltzmann constant `(k_(B))`, the absolute temperature (T), the number pr unit volume (n) of certain charged paticles, and the charge (q) carried by each of the particles. Which of the following expression for l is dimensionally correct?

A

`l=sqrt((nq^(2))/(epsilonk_(B)T))`

B

`l=sqrt((epsilonk_(0)T)/(nq^(2)))`

C

`l=sqrt((q^(2))/(epsilon n^((2)/(3))k_(B)T))`

D

`l=sqrt((q^(2))/(epsilon n k_(B)T))`

Text Solution

Verified by Experts

The correct Answer is:
B
Dimension of `(q^(2))/(kTepsilon_(0)r)=L`
Dimension of `n=L^(-3)`
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