Potential Energy Path Independence in Electrostatics

 

❓ Concept

Charge circular path pe move kare,

curve dikhe, arc dikhe…

👉 Par JEE poochta hai sirf start aur end ka khel! ⚡🧠

Electrostatics ka yeh golden rule pakad liya,
toh half chapter khud simplify ho jaata hai 🔥

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🖼️ Concept Image

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✍️ Short Explanation

Electrostatic force conservative hoti hai.
Matlab energy change path pe depend nahi karta.

Isliye circular path sirf distraction hai 😎

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🔹 Step 1 — Key Rule: Electrostatic Force is Conservative (FOUNDATION 💯)**

Electrostatic field ka sabse powerful rule:

$$\Delta U = U_f - U_i$$

👉 Depends only on:

• Initial position

• Final position

❌ Path does NOT matter

Circular, zig-zag, straight — sab same.

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🔹 Step 2 — Potential Energy Change Formula

For a charge $q_3$ placed in electric field:

$$\Delta U = q_3 (V_f - V_i)$$

⚡ Sirf potential difference important hai.

Force ka work = potential energy change.

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🔹 Step 3 — Electric Potential Depends on Distance Only

For point charge:

$$V = \frac{kq}{r}$$

Important:

• Direction irrelevant

• Angle irrelevant

• Arc length irrelevant

👉 Sirf distance $r$ matter karta hai.

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🔹 Step 4 — Multiple Charges ⇒ Superposition

If two charges $q_1, q_2$ present:

$$V_{\text{total}} = V_1 + V_2$$

So:

$$\Delta U = q_3 \left[ (V_{1f}+V_{2f}) - (V_{1i}+V_{2i}) \right]$$

📌 Always add potentials first, then multiply by $q_3$.

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🔹 Step 5 — Circular Path = Red Herring 🎭

JEE circular path isliye dikhata hai
taaki confuse ho jao 😄

Truth:

Even if radius constant ho,
distance from each charge constant nahi hota.

👉 Bas initial & final distances check karo.
Problem khatam ✔️

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⭐ Golden Summary Box

• Electrostatic force = conservative

• $\Delta U = q(V_f - V_i)$
  

• Potential depends only on distance

• Superposition applies

• Path = distraction