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The quantities $x = \frac{1}{\sqrt{μ_{0} \in_{0}}}, y = \frac{E}{B}$ and $z = \frac{l}{C R}$ are defined where C-capacitance, R-Resistance, $l$ -length, E-Electric field, B-magnetic field and $\in_{0}, μ_{0} -$ free space permittivity and permeability respectively. Then :

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Only x and z have the same dimension

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x,y and z have the same dimension

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detailed solution

Correct option is D

x=1μ0ε0⇒dimensional formula of x=M0L1T−1y=EB⇒y=M0L1T−1,z=LT=L1T−1So all quantities have same dimensional formula of velocity or speed.

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The quantities x=1μ0∈0,y=EB and z=lCR are defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and ∈0,μ0−free space permittivity and permeability respectively. Then :

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The quantities $x = \frac{1}{\sqrt{μ_{0} \in_{0}}}, y = \frac{E}{B}$ and $z = \frac{l}{C R}$ are defined where C-capacitance, R-Resistance, $l$ -length, E-Electric field, B-magnetic field and $\in_{0}, μ_{0} -$ free space permittivity and permeability respectively. Then :