A physical quantity S→ is defined as S→=(E→×B→)/μ0, where E→ is electric field, B→ is magnetic field and μ0 is the permeability of free space. The dimensions of S→ are the same as the dimensions of which of the following quantity (ies) ?

Force Length × Time , Power Area

A physical quantity S→ is defined as S→=(E→×B→)/μ0, where E→ is electric field, B→ is magnetic field and μ0 is the permeability of free space. The dimensions of S→ are the same as the dimensions of which of the following quantity (ies) ?

S ¯ = E ¯ × B ¯ μ 0 = [ S ] = [ E ] [ B ] μ 0 = [ CB ] [ B ] μ 0 = B 2 μ 0 [ C ] B 2 μ 0 has dimensions of energy density ∴ [ S ] = [ energy [ speed ] ] [ volume ] = ML 2 T − 2 L 3 LT − 1 = MT − 3

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A physical quantity $\vec{S}$ is defined as $\vec{S} = (\vec{E} \times \vec{B}) / μ_{0},$ where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and μ₀ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies) ?

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$\frac{Energy}{Ch arg e \times Current}$

$\frac{Force}{Length \times Time}$

$\frac{Energy}{Volume}$

$\frac{Power}{Area}$

answer is B, D.

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Detailed Solution

$\begin{array}{l} \bar{S} = \frac{\bar{E} \times \bar{B}}{μ_{0}} = \\ [S] = \frac{[E] [B]}{[μ_{0}]} = \frac{[CB] [B]}{[μ_{0}]} = [\frac{B^{2}}{μ_{0}}] [C] \end{array}$