A length-scale ( l l l ) depends on the permittivity (ε) of a dielectric material, Boltzmann constant kB, 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 expressions(s) for l l l is(are) dimensionally correct?
Physics · Electrostatic
JEE Advanced 2016

Question

A length-scale ( l l l ) depends on the permittivity (ε) of a dielectric material, Boltzmann constant kB, 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 expressions(s) for l l l is(are) dimensionally correct?

Physics · Electrostatic

JEE Advanced 2016

G1 Physics · Accepted Answer

Step 1: Identify the relevant electrostatic principle—Coulomb's law, superposition, Gauss's law, potential-energy conservation or conductor boundary conditions. Step 2: Write the corresponding equation using the quantities in the question and simplify the geometry. Step 3: Substitute the given values and compare with the alternatives. Final: Option B; Option D.