JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Units & Measurement

The quantities

x = \frac{1}{μ _{0} ϵ _{0}}, y = \frac{E}{B}

and

z = \frac{l}{C R}

are defined where

C

-capacitance,

R

Resistance,

l

-length,

E

-Electric field,

B

-magnetic field and

ϵ_{0}

μ_{0}

, - free space permittivity and permeability respectively. Then:

Answer: (A)

Solution

Each quantity turns out to be a speed. The combination

x = \frac{1}{μ _{0} ϵ _{0}}

is the speed of light, with dimensions

[L T^{- 1}]

. The ratio

y = \frac{E}{B}

is the speed of an electromagnetic wave, again

[L T^{- 1}]

. In

z = \frac{l}{C R}

the product

C R

is a time constant, so a length divided by a time is once more

[L T^{- 1}]

. All three share the dimensions of velocity.

JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Single correct option