Question 288: Units , Dimensions and Error Analysis

Question

A physical quantity $$\overrightarrow S $$ is defined as $$\overrightarrow S  = (\overrightarrow E  	imes \overrightarrow B )/{\mu _0}$$, where $$\overrightarrow E $$ is electric field, $$\overrightarrow B $$ is magnetic field and $$\mu$$
0
is the permeability of free space. The dimensions of $$\overrightarrow S $$ are the same as the dimensions of which of the following quantity(ies)?

Accepted Answer

Dimension of electric field $$[E] = [M{A^{ - 1}}L{T^{ - 3}}]$$
Dimensions of magnetic field [B]
$$[B] = [M{A^{ - 1}}L{T^{ - 2}}]$$
Dimensions of magnetic permebility
$$[{\mu _0}] = [M{A^{ - 2}}{T^{ - 2}}L]$$
$$[S] = {{EB} \over {{\mu _0}}} = {{[M{A^{ - 1}}L{T^{ - 3}}][M{A^{ - 1}}{T^{ - 2}}]} \over {[M{A^{ - 2}}{T^{ - 2}}L]}} = [M{T^{ - 3}}]$$

Answer

$${{Energy} \over {Ch\arg e 	imes Current}}$$

Answer

$${{Force} \over {Length 	imes Time}}$$

Answer

$${{Energy} \over {Volume}}$$

Answer

$${{Power} \over {Area}}$$

Units , Dimensions and Error Analysis

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