Physics Q26 – JEE-MAIN 2025

ϵ_{0}

denotes the permittivity of free space and

Φ_{E}

is the flux of the electric field through the area bounded by the closed surface, then dimensions of

(ϵ_{0} \frac{d Φ_{E}}{d t})

are that of :

Clue 1 of 3: Fundamental Laws

Recall Gauss's Law for electrostatics, which relates electric flux to enclosed charge and permittivity.

🥷

Ninja Strategy•Recognize Displacement Current

The expression $ϵ_{0} \frac{d Φ_{E}}{d t}$ is precisely the definition of Maxwell's displacement current, which by its nature has the dimensions of electric current.

🧠 Full Solution Path

Step 1: Relate Electric Flux to Charge✦ Active

According to Gauss's Law for electricity, the electric flux $Φ_{E}$ through a closed surface is related to the enclosed charge $Q_{e n c}$ and the permittivity of free space $ϵ_{0}$ by the formula:

Φ_{E} = \frac{Q_{e n c}}{ϵ_{0}}

Rearranging this, we get:

Q_{e n c} = ϵ_{0} Φ_{E}

Step 2: Differentiate with Respect to Time○ Expand

Differentiating the expression for $Q_{e n c}$ with respect to time $t$ :

\frac{d Q_{e n c}}{d t} = ϵ_{0} \frac{d Φ_{E}}{d t}

The term $\frac{d Q_{e n c}}{d t}$ represents the rate of change of charge, which is defined as electric current ( $I$ ). The term $ϵ_{0} \frac{d Φ_{E}}{d t}$ is known as the displacement current ( $I_{D}$ ). Therefore, the given expression is equivalent to electric current.

💡 Teacher's Secret Hint

Remember that the time derivative of charge is current.

Step 3: Determine Dimensions○ Expand

Since $ϵ_{0} \frac{d Φ_{E}}{d t}$ is equal to electric current, its dimensions must be the same as the dimensions of electric current. The dimension of electric current is $[A]$ (Ampere).

[ϵ_{0} \frac{d Φ_{E}}{d t}] = [I] = [A]

💡 Teacher's Secret Hint

Alternatively, you can derive the dimensions of each component ( $ϵ_{0}$ , $Φ_{E}$ , $t$ ) and multiply them out to confirm the final dimension.

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Physics Question 26 – JEE-MAIN 2025

Clue 1 of 3: Fundamental Laws

🧠 Full Solution Path