A physical quantity is defined as where is electric field, is magnetic field and is the permeability of free space. The dimensions of are the same as the dimensions of which of the following quantities? [2021]

Question

A physical quantity $\vec{S}$ is defined as $\vec{S} = \frac{(\vec{E} \times \vec{B})}{μ_{0}},$ where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $μ_{0}$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantities? [2021]

Smart Achievers · Accepted Answer

(2, 4)

Given physical quantity,

$\vec{S} = [\vec{E} \times \vec{B}] \frac{1}{μ_{0}}$

Here $\vec{E}$ is known as poynting vector and it represents flow of energy per unit area per unit time

$\vec{S} = \frac{Energy}{Area \times Time} = \frac{Power}{Area} = \frac{Force}{Length \times Time}$

Solution

1 $\frac{Energy}{Charge \times Current}$

2 $\frac{Force}{Length \times Time}$

3 $\frac{Energy}{Volume}$

4 $\frac{Power}{Area}$

Ans.
(2, 4)

Given physical quantity,

$\vec{S} = [\vec{E} \times \vec{B}] \frac{1}{μ_{0}}$

Here $\vec{S}$ is known as poynting vector and it represents flow of energy per unit area per unit time

$\vec{S} = \frac{Energy}{Area \times Time} = \frac{Power}{Area} = \frac{Force}{Length \times Time}$

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Solution

Q. 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 quantities [2021]

1 EnergyCharge×Current

2 ForceLength×Time

3 EnergyVolume

4 PowerArea