A length-scale (J) depends on the permittivity ($$ε$$) 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?

A

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

B

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

C

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

D

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