Match List I with List II. List I: (a) Capacitance, C (b) Permittivity of free space, $\varepsilon_{0}$ (c) Permeability of free space, $\mu_{0}$ (d) Electric field, E List II: (i) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}$ (ii) $\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}$ (iii) $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{~A}^{2}$ (iv) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2} \mathrm{~A}^{-2}$ Choose the correct answer from the options given below:

Capacitance follows from : Permittivity follows from Coulomb's law : Permeability follows from : Electric field follows from : So capacitance has dimensions , permittivity of free space , permeability of free space and electric field .

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Units & Measurement

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Match List I with List II.

List I:
(a) Capacitance, C
(b) Permittivity of free space,

ε_{0}

μ_{0}

(d) Electric field, E

List II:
(i)

M^{1} L^{1} T^{- 3} A^{- 1}

(ii)

M^{- 1} L^{- 3} T^{4} A^{2}

(iii)

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

(iv)

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

Choose the correct answer from the options given below:

Answer: A → III, B → II, C → IV, D → I

Solution

Capacitance follows from

C = \frac{Q}{V} = \frac{Q ^{2}}{W}

[C] = \frac{A ^{2} T ^{2}}{M L ^{2} T ^{- 2}} = M^{- 1} L^{- 2} T^{4} A^{2}

Permittivity follows from Coulomb's law

F = \frac{q _{1} q _{2}}{4 π ε _{0} r ^{2}}

[ε_{0}] = \frac{A ^{2} T ^{2}}{ML T ^{- 2} \cdot L ^{2}} = M^{- 1} L^{- 3} T^{4} A^{2}

Permeability follows from

c = \frac{1}{μ _{0} ε _{0}}

[μ_{0}] = \frac{1}{[ ε _{0} ] [ c ] ^{2}} = M^{1} L^{1} T^{- 2} A^{- 2}

Electric field follows from

E = \frac{F}{q}

[E] = \frac{ML T ^{- 2}}{AT} = M^{1} L^{1} T^{- 3} A^{- 1}

So capacitance has dimensions

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

, permittivity of free space

M^{- 1} L^{- 3} T^{4} A^{2}

, permeability of free space

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

and electric field

M^{1} L^{1} T^{- 3} A^{- 1}

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Match the columns

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JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Units & Measurement

Solution

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