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JEE Advanced 2016
Paper-1 2016
Multiple correct answers - Select all that apply
Question
A length-scale $(\ell)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzman constant $\left(\mathrm{k}_{\mathrm{B}}\right)$, 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 $\ell$ is(are) dimensionally correct?
Select ALL correct options:
A
$I=\sqrt{\left(\frac{\mathrm{nq}^2}{\varepsilon \mathrm{k}_{\mathrm{B}} \mathrm{T}}\right)}$
B
$I=\sqrt{\left(\frac{\varepsilon K_B T}{n q^2}\right)}$
C
$I=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$
D
$I=\sqrt{\left(\frac{q^2}{e n^{1 / 3} k_B T}\right)}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
⚠ Partially correct. Some answers are missing.
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