A length -scale \( (l) \) depends on the permittivity \( (\varepsilon) \) of a dielectric materi...

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A length -scale \( (l) \) depends on the permittivity \( (\varepsilon) \) of a dielectric material, Boltzmann constant \( \left(\left(k_{B}\right)\right. \), 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 \( / \) is (are) dimensionally correct?
(A) \( l=\sqrt{\left(\frac{n q^{2}}{\varepsilon k_{B} T}\right)} \)
(B) \( l=\sqrt{\left(\frac{\varepsilon k_{B} T}{n q^{2}}\right)} \)
(C) \( l=\sqrt{\left(\frac{q^{2}}{\varepsilon n^{2 / 3} k_{B} T}\right)} \)
(D) \( l=\sqrt{\left(\frac{q^{2}}{\varepsilon n^{1 / 3} k_{B} T}\right)} \)
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