A length-scale ( ) depends on the permittivity ( ) of a dielectric material,…

PHYSICS · Single correct · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

A length-scale (

l

) depends on the permittivity (

\epsilon

) of a dielectric material, Boltzmann constant (

k_B

), the absolute temperature (

T

), the number per unit volume (

n

) of certain charged particles, and the charge (

q

) carried by each of the particles. Which of the following expression(s) for

l

is(are) dimensionally correct? [Adv. 2016] (1)

l = \sqrt{\left(\frac{nq^2}{\epsilon k_B T}\right)}

(2)

l = \sqrt{\left(\frac{\epsilon k_B T}{nq^2}\right)}

(3)

l = \sqrt{\left(\frac{q^2}{\epsilon n^{2/3} k_B T}\right)}

(4)

l = \sqrt{\left(\frac{q^2}{\epsilon n^{1/3} k_B T}\right)}