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JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2020
- Hard
- MCQ
The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then....
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(x, y\) and \(z\) have the same dimension
Step-by-step Solution
Detailed explanation
\(x =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}=\operatorname{speed} \Rightarrow[ x ]=\left[ L ^{1} T ^{-1}\right]\)
\(y =\frac{ E }{ B }=\operatorname{speed} \Rightarrow[ y ]=\left[ L ^{1} T ^{-1}\right]\)
\(z=\frac{\ell}{R C}=\frac{\ell}{\tau} \Rightarrow[z]=\left[L^{1} T^{-1}\right]\)
So, \(x, y, z\) all have the same dimensions.
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