The unit of sqrt(2I/(epsilon_0 c)) is : (I= intensity of an electromagnetic wave, c: speed of light)

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q39 – JEE-MAIN 2025

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Home Physics EM WavesQuestion #178

The unit of

\sqrt{\frac{2 I}{ϵ_{0} c}}

is : (

I =

intensity of an electromagnetic wave,

c :

speed of light)

Clue 1 of 3: Conceptual Principle

Consider the fundamental relationship between the intensity of an electromagnetic wave and its electric field strength.

🥷

Ninja Strategy•Recognize the Electric Field

The given expression directly corresponds to the electric field strength of an electromagnetic wave, whose standard unit is $N / C$ or $V / m$ .

🧠 Full Solution Path

Step 1: Identify the Physical Quantity✦ Active

The intensity $I$ of an electromagnetic wave is related to its peak electric field strength $E_{0}$ by the formula:

I = \frac{1}{2} ϵ_{0} c E_{0}^{2}

Rearranging this formula to solve for $E_{0}$ , we get:

E_{0}^{2} = \frac{2 I}{ϵ_{0} c} ⟹ E_{0} = \sqrt{\frac{2 I}{ϵ_{0} c}}

Thus, the expression given in the question represents the peak electric field strength ( $E_{0}$ ) of an electromagnetic wave.

Step 2: Determine the Unit of Electric Field○ Expand

The standard unit for electric field strength ( $E$ ) is Volt per meter ( $V / m$ ) or Newton per Coulomb ( $N / C$ ). These two units are equivalent.

To show equivalence: $V = J / C$ and $J = N \cdot m$ . So, $V / m = (J / C) / m = (N \cdot m) / (C \cdot m) = N / C$ .

Step 3: Match with Options○ Expand

Now, we compare the unit of electric field ( $N / C$ ) with the given options:

1. $V m$ (Volt-meter): This is a unit of electric potential multiplied by distance.

2. $N C^{- 1}$ (Newton per Coulomb): This is equivalent to $N / C$ , which is a unit of electric field.

3. $N C$ (Newton-Coulomb): This is a unit of force multiplied by charge.

4. $N m$ (Newton-meter): This is a unit of work or energy (Joule).

Therefore, the correct option is $N C^{- 1}$ .

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Physics Question 39 – JEE-MAIN 2025

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path