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

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A length-scale \( (l) \) depends on the permittivity \( (\varepsilon) \) of a dielectric material, Boltzmanns constant \( \left(k_{B}\right) \), 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 \( l \) 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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