Verified Solution • 2025–26 Session moderate

QJEEM21Phd368: JEE Main 2021 Physics - Class 12 JEEM21Phd368 Solution: Match List I with List II. List - I List - II (a) Capacitance,…

Match List I with List II.

	List - I		List - II
(a)	Capacitance, C	(i)	${M^1}{L^1}{T^{ - 3}}{A^{ - 1}}$
(b)	Permittivity of free space, ${\varepsilon _0}$	(ii)	${M^{ - 1}}{L^{ - 3}}{T^4}{A^2}$
(c)	Permeability of free space, ${\mu _0}$	(iii)	${M^{ - 1}}{L^{ - 2}}{T^4}{A^2}$
(d)	Electric field, E	(iv)	${M^1}{L^1}{T^{ - 2}}{A^{ - 2}}$

Choose the correct answer from the options given below

Multiple Choice Options

A (a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
B (a) $\to$ (iii), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (i)
C (a) $\to$ (iv), (b) $\to$ (ii), (c) $\to$ (iii), (d) $\to$ (i)
D (a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (ii), (d) $\to$ (i)

Step-by-Step Verified Solution

q = CV

[C] = \left[ {{q \over V}} \right] = {{(A \times T)} \over {M{L^2}{T^{ - 2}}}}

= {M^{ - 1}}{L^{ - 2}}{T^4}{A^2}

[E] = \left[ {{F \over q}} \right] = {{ML{T^{ - 2}}} \over {AT}}

= ML{T^{ - 3}}{A^{ - 1}}

F = {{{q_1}{q_2}} \over {4\pi { \in _0}{r^2}}}

[{ \in _0}] = {M^{ - 1}}{L^{ - 3}}{T^4}{A^2}

Speed of light

c = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}

{\mu _0} = {1 \over {{ \in _0}{c^2}}}

[{\mu _0}] = {1 \over {{M^{ - 1}}{L^{ - 3}}{T^4}{A^2}]{{[L{T^{ - 1}}]}^2}}}

= [{M^1}{L^1}{T^{ - 2}}{A^{ - 2}}]

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