🌀 Flux & Induction — Interactive
Visualize Electromagnetic Induction
Lenz's Law, motional EMF, and mutual induction — animated live on canvas. See the physics, don't just read it.
🧲 Lenz's Law — Magnet & Coil Interaction
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Magnetic Flux (Wb)
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Induced EMF (V)
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Current Direction
What you're seeing: A bar magnet oscillating toward and away from a conducting coil. As flux through the coil changes, an EMF is induced. Watch how the current direction reverses when the magnet changes direction — Lenz's Law in action.
🧠 Reading the Visualizer
Magnet approaching (flux increasing): Induced current creates B opposing the external B → current in one direction.
Magnet receding (flux decreasing): Induced current tries to maintain flux → current reverses.
Magnet stationary: No change in flux → no EMF → no current. (This is where students get confused — a static magnet, even if inside the coil, induces zero EMF.)
Magnet receding (flux decreasing): Induced current tries to maintain flux → current reverses.
Magnet stationary: No change in flux → no EMF → no current. (This is where students get confused — a static magnet, even if inside the coil, induces zero EMF.)
🔄 Mutual Inductance — Primary & Secondary Coil
Mutual Induction: Alternating current in the primary coil creates a changing magnetic field. This changing field passes through the secondary coil and induces an EMF in it — even though the secondary is not physically connected. This is the transformer principle.
📐 Magnetic Flux Interactive — Vary B, A, θ
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Φ = BA cosθ (Wb)
✋ Right Hand Thumb Rule
- Curl the fingers of your right hand around the wire/coil
- Point the thumb in the direction of conventional current
- Fingers curl in the direction of magnetic field (B) around the wire
- For coil: thumb points in direction of B through the coil
💡 Used to find B direction from current direction in solenoid
🤚 Right Hand (for Motional EMF)
- Point fingers in direction of velocity (v) of the rod
- Curl them toward B (magnetic field direction)
- The thumb points in direction of induced current in rod
- Alternatively: F = qv×B → direction of force on positive charge
💡 Used for direction in rail problems and rotating rods
🧲 Fleming's Right Hand Rule (Generator)
- Thumb: direction of motion of conductor
- Index finger: direction of magnetic field (B)
- Middle finger: direction of induced current
- All three mutually perpendicular
💡 Used specifically for generators and dynamos
4-Step Lenz's Law Method
- Identify if flux is increasing or decreasing
- Identify direction of original magnetic field (B)
- Induced B opposes the change (if Φ↑, induced B opposes original)
- Use right-hand rule to get current direction from induced B
💡 Works for every direction problem in all exams
📊 Case-by-Case Analysis — EMF Generation Mechanisms
Case 1: Changing B, Fixed Loop
Φ = BA cosθ. If B changes: dΦ/dt = A cosθ · (dB/dt). EMF = −N · A · cosθ · (dB/dt). Common in transformer cores. B changes due to AC current.
Case 2: Fixed B, Changing Area
Φ = BA cosθ. If A changes: dΦ/dt = B cosθ · (dA/dt). Example: expanding or contracting loop. Used in motional EMF derivation for rail problems.
Case 3: Fixed B and A, Changing θ
Φ = BA cosθ. If θ changes: dΦ/dt = −BA sinθ · (dθ/dt) = −BAω sinωt. This gives ε = NBAω sinωt — the AC generator equation.
Case 4: All Three Changing
JEE Advanced: dΦ/dt = (dB/dt)A cosθ + B(dA/dt)cosθ − BAsinθ(dθ/dt). Each term contributes separately. Add them algebraically.
🔬 JEE Insight — Static B ≠ Zero EMF (if area changes)
This is where most students lose marks. A static magnetic field can still induce EMF if the loop area is changing. Example: a loop being pulled out of a magnetic field region — B is constant, but as the loop exits, the effective area inside the field decreases → flux decreases → EMF induced. Always check which component of Φ = BAcosθ is changing.
❌ Critical Mistake — Uniform B inside solenoid
When a changing current flows in a solenoid, the B inside is uniform and changes with time. The EMF induced in a loop INSIDE the solenoid depends on its own area — not the solenoid cross-section. The EMF induced in a loop OUTSIDE is zero (B = 0 outside ideal solenoid). This distinction catches most students in JEE Main.