Pages

 

Electrostatics – Stage 2 (Page 6)

Electric Potential Energy & System of Charges

1️⃣ What is Electric Potential Energy?

Electric potential energy (U) of a charge is the work done in assembling the charge configuration against electrostatic forces.

U = qV

Where V is the electric potential at the position of charge q.

👉 Scalar quantity, depends on position.

2️⃣ Potential Energy of Two Point Charges

For two charges q₁ and q₂ separated by distance r:

U = 1/(4πε₀) · (q₁q₂ / r)

  • Like charges → U positive (repulsion)
  • Unlike charges → U negative (attraction)

⚠️ Zero reference taken at infinity.

3️⃣ Potential Energy of a System of Charges

For multiple charges, total potential energy is the sum of pairwise interactions.

U = Σ 1/(4πε₀) · (qᵢqⱼ / rᵢⱼ)

Sum over all distinct pairs.

👉 No self-energy included.

4️⃣ Potential Energy of a Charge in External Field

If a charge q is placed in an external potential V:

U = qV

Used heavily in capacitor and motion-based problems.

5️⃣ Relation Between Force and Potential Energy

Electrostatic force is the negative gradient of potential energy.

F = − dU / dr

  • Stable equilibrium → U minimum
  • Unstable equilibrium → U maximum

⚠️ Equilibrium questions are favorite in JEE Advanced.

6️⃣ Energy Conservation in Electrostatics

In electrostatic field:

  • Total energy (KE + PE) conserved
  • Only conservative forces act

ΔK = − ΔU

Used to find speed of charged particle.

7️⃣ Typical IIT Problem Insight

Q: A charge is released from rest near another charge. How to find speed?

Approach:

  • Find initial PE
  • Find final PE
  • Use energy conservation

8️⃣ Comparison Table (Quick Recall)

Quantity Depends On Nature
Electric Field (E) Test charge independent Vector
Potential (V) Position Scalar
Potential Energy (U) Charge + position Scalar

9️⃣ Common Mistakes (Avoid in Exam)

  • Forgetting pair counting in multi-charge systems
  • Mixing V and U incorrectly
  • Wrong reference level

What’s Next?

👉 Stage 2 – Page 7:
Capacitors – Basic Theory & Capacitance

📘 IIT–JEE Physics Complete Master Library (Class XI & XII)

Concepts • Problems • Advanced Applications • Thinking Skills
Designed for IIT–JEE (Main & Advanced)

🧠 Physics Thinking & Foundation

⚙️ Mechanics (Class XI)

🔁 Oscillations & Thermal Physics

⚡ Electrostatics (Class XII – Stage-wise)

🔹 Stage 0 – Foundation

🔹 Stage 1 – Core Concepts

🔹 Stage 2 – Applications

🔹 Stage 3 – Advanced (IIT JEE)

🔌 Current Electricity

🌐 Master Navigation

© Mind Grow Magazine | IIT–JEE Physics Learning Ecosystem

at

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)

UPSC Geography Synopsis Hindi Mega Learning Library 2026 – Complete Revision Hub

   Explore More: Hindi Geography Library | English GS Library | Telugu UPSC Library  UPSC Geography Synopsis Hind...

  • Intermediate Physics Complete Notes | IIT JEE Physics Study Material
      Intermediate Physics Complete Notes – IIT JEE & Board Exams This page contains complete Intermediate Physics notes along wit...
  • (no title)
      📘 Physics Complete Library 🧠 How IIT Toppers Think 📚 Physics Thinking Library – How IIT Toppers Think ...
  • (no title)
      📘 IIT–JEE Physics Complete Master Library (Class XI & XII) Concepts • Problems • Advanced Applications • Thinking Skill...