JEE Advanced_2016_S1 ( Physics 2016 Q-7 ) - Competishun – Live JEE & NEET Courses and Exam Prep

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:

$I=\sqrt{\left(\frac{\mathrm{nq}^2}{\varepsilon \mathrm{k}_{\mathrm{B}} \mathrm{T}}\right)}$

$I=\sqrt{\left(\frac{\varepsilon K_B T}{n q^2}\right)}$

$I=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$

$I=\sqrt{\left(\frac{q^2}{e n^{1 / 3} k_B T}\right)}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution