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A length scale (l) depends on the permittivity of a (ε) dielectric material,Boltzmann constant( kB) ,the absolute temperature(T),the number per unit volume (n) of charged particles, and the charge (q) carried by each of the particles. which of the following is dimensionally correct a) l = √[(nq^2)÷( εkBT)] b) l = √[( εkBT) ÷ (nq^2) ] c) l =√[(q^2)÷ (εnkBT)]

A length scale (l) depends on the permittivity of a (ε) dielectric material,Boltzmann constant( kB) ,the absolute temperature(T),the number per unit volume (n) of charged particles, and the charge (q) carried by each of the particles. which of the following is dimensionally correct                             a) l = √[(nq^2)÷( εkBT)]                                                  b) l = √[( εkBT) ÷ (nq^2) ]                                              c) l =√[(q^2)÷ (εnkBT)]

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

F=\dfrac{1}{4\pi\epsilon}\dfrac{q^2}{d^2}

Henced=\dfrac{q^2}{4\pi\epsilon Fd}

Fd has dimennsion of work which is that of energy , which is that ofnk_BT

Hence[l]=[\dfrac{nq^2}{\epsilon nK_BT}]

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