Displacement Current Concept — Dimensions Made Easy ⚡

 

❓ Concept

🎬 EM Waves: Dimension of $\varepsilon_0 \dfrac{d\Phi_E}{dt}$ in 59 Sec

Electric flux ka time-rate diya ho…
aur uske saath $\varepsilon_0$ multiply ho raha ho…

👉 Toh sawal sirf maths ka nahi hai —
physics ka meaning samajhne ka hai ⚡🤔

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🖼️ Concept Image

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✍️ Short Explanation

JEE is concept ko isliye pyaar karta hai kyunki yahin se
Maxwell equations aur EM waves ka foundation banta hai.

Agar tumhe yeh samajh aa gaya,
👉 dimensions + theory dono clear.

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🔹 Step 1 — Electric Flux Meaning (FOUNDATION 💯)**

Electric flux:

$${\mathrm{\Phi }}_E=\oint \vec{E}\cdot d\vec{A}$$

So dimensionally:

• Electric field $E$
  

• Area $A$
  

$$[{\mathrm{\Phi }}_E]=[E]\times [\text{Area}]$$

📌 Matlab:
Flux measures how much electric field passes through a surface.

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🔹 Step 2 — Time Rate of Electric Flux

$$\frac{d{\mathrm{\Phi }}_E}{d\mathrm{t<span\; class="vlist-s"></span>}}$$

Iska matlab:

• Electric field time ke saath change ho raha hai

• Ya surface ke through field flow vary kar raha hai

📌 Yeh quantity batati hai:

Electric field kitni tezi se badal raha hai

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🔹 Step 3 — Role of $\varepsilon_0$ (MOST IMPORTANT 🔥)**

Maxwell ki correction ke according:

$$\varepsilon_0 \frac{d\Phi_E}{dt}$$

👉 Isko kehte hain Displacement Current.

Important point:

• Yeh real charge flow nahi hai

• Lekin equations mein current ki tarah behave karta hai

📌 Yahin se Ampere–Maxwell law complete hota hai.

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🔹 Step 4 — Maxwell’s Big Insight (GAME CHANGER ⚡)**

Maxwell ne observe kiya:

• Conduction current (wire mein charge flow)

• Displacement current (changing electric field)

👉 Dono ka same effect hota hai magnetic field banane mein.

Isliye:

$$\text{Conduction current}⟷\text{Displacement current}$$

📌 Symmetry ka matlab:

$${\epsilon }_0\frac{d{\mathrm{\Phi }}_E}{dt}$$

ke dimensions = electric current.

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🔹 Step 5 — Golden Concept to Remember ⭐

🧠 One-line idea:

Electric field jab time ke saath badalta hai,
toh woh current ki tarah act karta hai.

Isliye:

$${\epsilon }_0\times (\text{rate of change of electric flux})\equiv \text{Displacement current}$$

Aur dimensionally:

$$\boxed{{\displaystyle \text{Electric Current}}}$$

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⭐ Golden Summary Box

• Electric flux ⇒ field through surface

• Time-rate of flux ⇒ changing electric field

• $\varepsilon_0$ multiply ⇒ Maxwell correction

• Quantity behaves like current

• Enables EM wave propagation

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✅ Final Takeaway

Is concept ke bina:

• Capacitor charging incomplete

• EM waves impossible

🧠 Maxwell ne flux ko current bana diya —
isi se light aur radio waves possible hui 🌊⚡