Mini Concept Problems – Field + Network Thinking (IIT Level)

Superposition • Gauss Law • Maxwell Insight • Capacitors • Inductors

SECTION 1 – Superposition Theorem (Electrostatics)

Problem 1 (Very Fundamental)

Two identical charges +q are placed at distance 2a apart. Find the electric field at the midpoint.

Thinking (NOT formula):

  • Field due to each charge is equal in magnitude
  • Directions are opposite

Answer: Electric field at midpoint = 0

IIT Insight: Superposition is vector cancellation, not algebra.

Problem 2 (Direction Trap)

Replace one charge by –q. What happens to the field at midpoint?

Thinking:

  • Field due to +q → away from +q
  • Field due to –q → towards –q
  • Both fields point in same direction

Answer: Field magnitude doubles.

IIT Trick: Opposite charges → fields ADD, forces confuse beginners.

SECTION 2 – Field Theory + Gauss Law

Problem 3 (Gauss Law Intuition)

A point charge +q is placed inside a hollow conducting sphere. What is the electric field inside the metal?

Thinking:

  • Charges rearrange on surface
  • Field inside conductor must be zero

Answer: Electric field inside conductor = 0

Gauss Law Core: Field inside conductor is zero in electrostatics.

Problem 4 (Gaussian Surface Trap)

Does electric field inside the cavity depend on where the charge is placed?

Answer: Yes, field inside cavity changes. But field inside conductor remains zero.

IIT Insight: Gauss law gives total flux, not local field everywhere.

SECTION 3 – Maxwell Thinking (Pre-JEE Advanced)

Problem 5 (Displacement Current Concept)

In a charging capacitor, is current flowing between plates?

Thinking:

  • No charge crosses dielectric
  • Electric field is changing

Answer: Conduction current = 0 Displacement current ≠ 0

Maxwell Genius: Changing electric field behaves like current.

Problem 6 (Ampere-Maxwell Law)

Why does magnetic field exist around a charging capacitor wire?

Answer:

  • Because current continuity is preserved
  • Displacement current completes the loop

SECTION 4 – Capacitor Mini Problems (Network View)

Problem 7 (Connection Change)

A capacitor is charged and then disconnected from battery. If plate separation increases, what happens to:

  • Charge?
  • Potential?
  • Energy?

Answer:

  • Charge → constant
  • Capacitance → decreases
  • Potential → increases
  • Energy → increases

IIT Rule: Disconnected battery → charge fixed.

Problem 8 (Battery Connected)

Same capacitor, battery still connected. Separation increases.

Answer:

  • Potential → constant
  • Charge → decreases
  • Energy → decreases

Network Thinking: Battery fixes potential like a voltage source.

SECTION 5 – Inductor Mini Problems (Energy + Field)

Problem 9 (Sudden Switch)

Current through an inductor cannot change instantly. Why?

Answer:

  • Inductor stores energy in magnetic field
  • Instant change requires infinite emf

Problem 10 (Energy View)

Where is energy stored in an inductor?

Answer: In the magnetic field around the coil.

Field View: Energy is never in the wire, always in the field.

FINAL IIT TAKEAWAY

  • Superposition = vector logic
  • Gauss = symmetry + flux
  • Maxwell = continuity of fields
  • Capacitors = potential networks
  • Inductors = magnetic energy buffers

Mastery Rule: If you understand these small problems deeply, big IIT problems collapse automatically.

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