Question 38: Units , Dimensions and Error Analysis

Question

If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :

Accepted Answer

The SI unit of permittivity of free space ( $\epsilon$ ) is derived from Coulomb's law $\left(F=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2}ight)$. The SI unit is $C^2 / N$. $\mathrm{m}^2$.
The electric field (E) is defined as force per unit charge, so its SI unit is Newtons per Coulomb (N/C).
The standard SI unit is the second (s).
The given expression is $\frac{\epsilon \mathrm{E}}{\mathrm{t}}$.
So, the SI unit of given expression is, $\frac{\mathrm{C}^2}{\mathrm{~N} \cdot \mathrm{~m}^2} 	imes\left(\frac{\mathrm{N}}{\mathrm{C}}ight)=\frac{\mathrm{C}}{\mathrm{s}}=\frac{\mathrm{s}}{\mathrm{s} \cdot \mathrm{m}^2}$
Electric current is defined as the rate of flow of electric charge over time. Therefore, 1 Ampere $(\mathrm{A})=$
1 Coulomb per second $\left(\frac{\mathrm{C}}{\mathrm{s}}ight)$.
Unit of $\frac{\epsilon \mathrm{E}}{\mathrm{t}}=\left(\frac{\mathrm{C}}{\mathrm{s}}ight) 	imes \frac{1}{\mathrm{~m}^2}=\mathrm{A} 	imes \frac{1}{\mathrm{~m}^2}=\mathrm{A} / \mathrm{m}^2$
Therefore, the SI unit of $\frac{\epsilon E}{t}$ is $\mathrm{A} / \mathrm{m}^2$. Hence, the correct option is (C).

Answer

Am

Answer

$\mathrm{A} / \mathrm{m}$

Answer

$\mathrm{A} / \mathrm{m}^2$

Answer

$\mathrm{Am}^2$

Units , Dimensions and Error Analysis

If \epsilon, E and t represent the free space permittivity, electric field and time respectively, then the unit of \frac{\epsilon E}{t} will be :

Choose the correct answer: