The quantities x = (1)/(√(μ₀ε₀)), y = E/B and z = l/CR are defined… | JEE Main 2020 (5 Sep, Shift 2)

Q74JEE Main 2020 · 5 SEP · SHIFT 2Medium

Units & Dimensions

The quantities x = $\frac{1}{\sqrt{\mu_0\varepsilon_0}}$ , y = $\frac{E}{B}$ and z = $\frac{l}{CR}$ are

defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $\varepsilon_0, \mu_0$ , - free space permittivity and permeability respectively. Then:

Show answer and solution

Answer: (b)

$x = \dfrac{1}{\sqrt{\mu_0\varepsilon_0}} = c$ , a speed $[\mathrm{LT^{-1}}]$ .
From $F = qE = qvB$ , $\dfrac{E}{B} = v$ , so $y = [\mathrm{LT^{-1}}]$ .
$CR$ is a time constant $[\mathrm{T}]$ , so $z = \dfrac{l}{CR} = [\mathrm{LT^{-1}}]$ .
So the answer is (b) x, y and z have the same dimension.

Report a mistake

More questions on Units & Dimensions

In SI units, the dimensions of √((ε₀)/(μ₀)) is:JEE Main 2019 (8 Apr, Shift 1)
Let, r, C and V represent inductance, resistance, capacitance and voltage, respectively…JEE Main 2019 (12 Jan, Shift 2)
[L²M¹T⁻²] are the dimensions ofMHT CET 2019 (3 May, Shift 1)
The dimensions of self or mutual inductance are given asMHT CET 2019 (2 May, Shift 2)
The ratio of the dimensions of Planck's constant to that of moment of inertia is the…MHT CET 2019 (2 May, Shift 2)
Dimensions of Gyromagnetic ratio areMHT CET 2019 (2 May, Shift 1)
Which of the following combinations has the dimension of electrical resistance ( ε 0 is…JEE Main 2019 (12 Apr, Shift 1)
In the following ‘I’ refers to current and other symbols have their usual meaning. Choose…JEE Main 2016 (9 Apr, Shift 1)

Units & Dimensions question from JEE Main 2020 (5 Sep, Shift 2)

More questions on Units & Dimensions