If ε, E and t represent the free space permittivity electric field and time respectively
Q. If $\varepsilon$, $E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\dfrac{\varepsilon E}{t}$ will be :

(A) A m

(B) A/m

(C) A/m2

(D) A m2

Correct Answer: A/m2

Explanation

Permittivity of free space $\varepsilon_0$ has SI unit

$$ \varepsilon_0 = \frac{\text{C}^2}{\text{N m}^2} $$

Electric field $E$ has SI unit

$$ E = \frac{\text{N}}{\text{C}} $$

Time $t$ has unit second (s).

Now consider the quantity

$$ \frac{\varepsilon E}{t} $$

Substituting units,

$$ \frac{\varepsilon E}{t} = \frac{\dfrac{\text{C}^2}{\text{N m}^2} \times \dfrac{\text{N}}{\text{C}}}{\text{s}} $$

Simplifying,

$$ = \frac{\text{C}}{\text{m}^2 \text{s}} $$

Since

$$ \frac{\text{C}}{\text{s}} = \text{A} $$

Therefore,

$$ \frac{\varepsilon E}{t} = \frac{\text{A}}{\text{m}^2} $$

Hence, the correct unit is

A/m2

Related JEE Main Questions

Given below are two statements : Statement I : For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :
An electric power line having total resistance of 2 Ω, delivers 1 kW of power at 250 V. The percentage efficiency of transmission line is ____.
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly ____ nm.
The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is 4/3. The wavelength of the same light when it is passing through a transparent medium having refractive index of 3/2 is ____ nm.
Home / Study Material

Updated for JEE Main 2026: This PYQ is important for JEE Mains, JEE Advanced and other competitive exams. Practice more questions from this chapter.

Scroll to Top