Units & Dimensions

JEE Main level, single correct, medium

104 of 149

Question 104 of 149

Match List I with List II. List-I List-II a Capacitance, C i M1L1T−3A−1{M}^{1}{L}^{1}{T}^{-3}{A}^{-1} b Permittivity of free space, ϵ0{\epsilon }_{0} ii M−1L−3T4A2{M}^{-1}{L}^{-3}{T}^{4}{A}^{2} c Permeability of free space, μ0{\mu }_{0} iii M−1L−2T4A2{M}^{-1}{L}^{-2}{T}^{4}{A}^{2} d Electric field, E iv M1L1T−2A−2{M}^{1}{L}^{1}{T}^{-2}{A}^{-2} Choose the correct answer from the options given below

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Answer: (A) (a)→(iii),(b)→(ii),(c)→(iv),(d)→(i)(a)\rightarrow (iii), (b)\rightarrow (ii),(c)\rightarrow (iv),(d)\rightarrow (i)

q=CVq=CV
[C]=[qV]=(A×T)2ML2T−2[C]=\left[\dfrac{q}{V}\right]=\dfrac{(A\times T{)}^{2}}{{ML}^{2}{T}^{-2}}
=M−1L−2T4A2={M}^{-1}{L}^{-2}{T}^{4}{A}^{2}
[E]=[Fq]=MLT−2AT[E]=\left[\dfrac{F}{q}\right]=\dfrac{{MLT}^{-2}}{AT}
=MLT−3A−1={MLT}^{-3}{A}^{-1}
F=q1q24π∈0r2F=\dfrac{{q}_{1}{q}_{2}}{4\pi {\in }_{0}{r}^{2}}
[ϵo]=M−1L−3T4A2\left[{ϵ}_{o}\right]={M}^{-1}{L}^{-3}{T}^{4}{A}^{2}
Speed of light c=1μ0∈oc=\dfrac{1}{\sqrt{{\mu }_{0}{\in }_{o}}}
μ0=1ϵ0c2{\mu }_{0}=\dfrac{1}{{ϵ}_{0}{c}^{2}}
[μ0]=1[M−1L−3T4A2][LT−1]2\left[{\mu }_{0}\right]=\dfrac{1}{\left[{M}^{-1}{L}^{-3}{T}^{4}{A}^{2}\right]{\left[{LT}^{-1}\right]}^{2}}
=[M1L1T−2A−2]=\left[{M}^{1}{L}^{1}{T}^{-2}{A}^{-2}\right]

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