Identify the physical parameters from the lis | vedclass

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(A) To determine which parameters have the same dimensions,we analyze each one:$(i)$ Magnetic field $(B)$: The force on a charge is $F = qvB$,so $[B]

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$(ii)$ and $(iv)$

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(A) To determine which parameters have the same dimensions,we analyze each one:$(i)$ Magnetic field $(B)$: The force on a charge is $F = qvB$,so $[B] = [F] / ([q][v]) = [MLT^{-2}] / ([IT][LT^{-1}]) = [MT^{-2}I^{-1}]$.$(ii)$ Energy density $(u)$: Energy per unit volume,$[u] = [ML^2T^{-2}] / [L^3] = [ML^{-1}T^{-2}]$.$(iii)$ Refractive index $(\mu)$: It is a ratio of speeds,so it is dimensionless $[M^0L^0T^0]$.$(iv)$ Young's modulus $(Y)$: Stress per unit strain,$[Y] = [ML^{-1}T^{-2}] / [1] = [ML^{-1}T^{-2}]$.$(v)$ Dielectric constant $(K)$: It is a ratio of permittivities,so it is dimensionless $[M^0L^0T^0]$.Comparing these,we see that $(ii)$ Energy density and $(iv)$ Young's modulus both have dimensions $[ML^{-1}T^{-2}]$,and $(iii)$ Refractive index and $(v)$ Dielectric constant are both dimensionless. Looking at the options,$(ii)$ and $(iv)$ share the same dimensions.

Identify the physical parameters from the list given below that have the same dimensions:
$(i)$ Magnetic field $(B)$
$(ii)$ Energy density $(u)$
$(iii)$ Refractive index $(\mu)$
$(iv)$ Young's modulus $(Y)$
$(v)$ Dielectric constant $(K)$

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Identify the physical parameters from the list given below that have the same dimensions:$(i)$ Magnetic field $(B)$$(ii)$ Energy density $(u)$$(iii)$ Refractive index $(\mu)$$(iv)$ Young's modulus $(Y)$$(v)$ Dielectric constant $(K)$