Lenz's Law - The Opposition Principle

Master Lenz's law and understand why nature always opposes change in magnetic flux - the key to predicting current direction in electromagnetic induction

11 min read

Movie Hook: Electromagnetic Braking in Bullet Trains

In high-speed trains like the Japanese Shinkansen or the Shanghai Maglev, there are no traditional brakes grinding metal on metal. Instead, they use electromagnetic braking based on Lenz’s law! When strong magnets move past metal plates, they induce currents that create opposing magnetic fields, slowing the train smoothly. It’s the same principle that helps the Iron Man suit make controlled landings - opposing forces from induced magnetic fields.

The Negative Sign Mystery

In Faraday’s law, we wrote:

$$\mathcal{E} = -N\frac{d\Phi_B}{dt}$$

Why the negative sign? This is where Lenz’s law comes in.

Lenz’s Law Statement

The direction of induced EMF (and hence induced current) is such that it opposes the change in magnetic flux that produced it.

Simple version: Nature doesn’t like change. When you try to increase flux, induced current creates flux to decrease it. When you try to decrease flux, induced current creates flux to increase it.

The Opposition Principle

Think of Lenz’s law as nature’s “resistance to change”:

If flux is increasing → Induced current creates field opposing the increase If flux is decreasing → Induced current creates field opposing the decrease

The induced magnetic field always tries to maintain the status quo.

Memory Trick: “Nature is LAZY”

Lenz’s law = Always opposes Zero Yield (the change)

Nature is lazy and doesn’t want things to change. The induced current flows in a direction to oppose whatever change you’re trying to make.

Why Lenz’s Law Follows Conservation of Energy

Imagine what would happen if Lenz’s law worked opposite (induced current assisted the change):

  1. You move magnet toward coil → Induced current creates field that pulls magnet faster
  2. Magnet accelerates → More flux change → More induced current
  3. More current → Stronger pull → Even faster acceleration
  4. Result: Infinite energy from nothing!

This violates energy conservation. Therefore:

Lenz’s Law = Conservation of Energy

The opposing force means you must do work to change the flux. This work is converted into electrical energy (induced current).

$$\text{Mechanical Work Input} = \text{Electrical Energy Output}$$

How to Apply Lenz’s Law: Step-by-Step

Method 1: Flux Change Method (Most Common)

Step 1: Identify if magnetic flux through loop is increasing or decreasing

Step 2: Determine direction of external magnetic field

Step 3: Apply Lenz’s law:

  • If flux increasing: Induced field opposes external field (opposite direction)
  • If flux decreasing: Induced field supports external field (same direction)

Step 4: Use right-hand thumb rule to find current direction that produces the induced field

Method 2: Force/Motion Method

Step 1: Identify the motion (magnet approaching, receding, etc.)

Step 2: Determine what force would oppose this motion

Step 3: Find current direction that creates this opposing force

Detailed Examples

Example 1: Bar Magnet Approaching a Coil

Scenario: North pole of magnet moves toward a coil from left.

Analysis:

  1. Flux through coil is increasing (more field lines entering)
  2. External field is toward right (from N to S)
  3. To oppose increase, induced field must be toward left (opposite)
  4. Induced field toward left requires current to be counterclockwise (viewed from magnet side)
  5. The coil’s left face becomes a North pole (repels approaching magnet)

Force: Repulsive (opposes approach) → You must push harder to move magnet

Approaching magnet: Same pole forms on near face (repulsion) Receding magnet: Opposite pole forms on near face (attraction)

Both cases oppose the motion!

Example 2: Magnet Leaving the Coil

Scenario: North pole of magnet moves away from coil toward right.

Analysis:

  1. Flux through coil is decreasing (field lines leaving)
  2. External field is toward right
  3. To oppose decrease, induced field must be toward right (same direction)
  4. Induced field toward right requires current to be clockwise (viewed from magnet side)
  5. The coil’s left face becomes a South pole (attracts receding magnet)

Force: Attractive (opposes recession) → Magnet experiences a drag

Right-Hand Rules for Direction

For Current Direction from Field Direction

Right-Hand Thumb Rule:

  • Curl fingers in direction of induced current
  • Thumb points in direction of induced magnetic field

For Force on Current

Fleming’s Left-Hand Rule: (for force on current-carrying conductor)

  • First finger: Field direction
  • Second finger: Current direction
  • Thumb: Motion/Force direction

Common JEE Problem Types

Type 1: Falling Magnet Through Coil

Problem: A bar magnet falls through a vertical coil. Compare falling speed to free fall.

Solution:

  1. As magnet enters: Flux increases → Induced current opposes motion → Upward force
  2. As magnet exits: Flux decreases → Induced current opposes motion → Upward force
  3. Net force is always upward (opposing gravity)
  4. Result: Magnet falls slower than free fall

Energy: Gravitational PE → Electrical energy + reduced KE

Type 2: Conductor Moving in Magnetic Field

Problem: A conducting rod moves on rails in perpendicular magnetic field.

Solution:

  1. As rod moves right, flux through circuit increases
  2. Induced current creates field opposing this increase
  3. Current direction: Using Lenz’s law or force analysis
  4. Force on rod (Fleming’s rule): Opposes motion (toward left)
  5. You must apply force to maintain constant velocity

Type 3: Expanding/Contracting Loops

Problem: A circular loop expands in a perpendicular magnetic field.

Solution:

  1. As area increases, flux increases
  2. Induced current opposes increase
  3. Induced field is opposite to external field
  4. Force on loop: Inward (opposes expansion)

The Negative Sign in Faraday’s Law

The negative sign in $\mathcal{E} = -N\frac{d\Phi_B}{dt}$ mathematically represents Lenz’s law:

If flux is increasing: $\frac{d\Phi_B}{dt} > 0$ → $\mathcal{E} < 0$ (negative EMF)

If flux is decreasing: $\frac{d\Phi_B}{dt} < 0$ → $\mathcal{E} > 0$ (positive EMF)

The sign tells us the EMF opposes the change.

Common Mistakes Students Make

❌ Mistake 1: Thinking induced field is always opposite to external field ✅ Reality: Induced field opposes the change, not necessarily the field itself

  • Flux increasing → Induced field opposes external field
  • Flux decreasing → Induced field supports external field

❌ Mistake 2: Confusing force direction with current direction ✅ Reality: Use separate rules:

  • Lenz’s law → Current direction
  • Fleming’s left-hand rule → Force direction

❌ Mistake 3: Forgetting that Lenz’s law is about opposing change ✅ Reality: Static fields produce no induction, regardless of strength

❌ Mistake 4: Applying right-hand rule incorrectly ✅ Reality:

  • Curl fingers along current
  • Thumb shows field direction inside the loop

❌ Mistake 5: Not considering energy conservation ✅ Reality: If you’re not sure, ask: “Does this violate energy conservation?”

Interactive Exploration

Experiment with:

  • Moving magnet toward/away from coil
  • Changing magnet strength
  • Reversing magnet polarity

Observe:

  • Current direction
  • Force on magnet
  • Energy transformations

Practice Problems

Level 1: JEE Main (Basics)

Problem 1.1: A bar magnet is dropped through a copper coil. Will it fall with acceleration g? Why?

Solution

Answer: No, it will fall with acceleration less than g.

Explanation:

  1. As magnet falls, flux through coil changes
  2. By Lenz’s law, induced current opposes this change
  3. The induced current creates a magnetic field that exerts an upward force on the magnet
  4. Net force: $F_{net} = mg - F_{induced}$
  5. Therefore: $a = g - \frac{F_{induced}}{m} < g$

The magnet experiences electromagnetic braking.

Energy consideration: Some gravitational PE converts to electrical energy (heating the coil), not all to KE.

Problem 1.2: The north pole of a bar magnet is pushed toward a metallic ring. Will the ring be attracted, repelled, or unaffected?

Solution

Answer: The ring will be repelled.

Explanation:

  1. As north pole approaches, flux through ring increases
  2. By Lenz’s law, induced current opposes this increase
  3. The induced current creates a magnetic field opposing the approaching field
  4. The near face of ring becomes a north pole
  5. Like poles repel → Ring is repelled

Key: The opposition to change manifests as opposition to the motion causing the change.

Level 2: JEE Advanced (Application)

Problem 2.1: A rectangular loop is placed partly in a magnetic field (perpendicular to plane, into page). The loop is pulled out with constant velocity. Find: (a) Direction of induced current (b) Direction of force needed to maintain constant velocity

Solution

Given: Loop pulled to the right, field into page, constant velocity v

(a) Direction of induced current:

  1. As loop exits, flux through loop decreases
  2. External field is into page
  3. To oppose decrease, induced field must be into page (same direction)
  4. Using right-hand rule: Curl fingers so thumb points into page
  5. Current direction: Clockwise (when viewed from above)

(b) Force needed:

  1. Current flows in the part of loop still in field
  2. Using Fleming’s left-hand rule:
    • Field: Into page
    • Current: Downward (left edge in field)
    • Force: Toward left (opposes motion)
  3. To maintain constant velocity, applied force must be toward right

Key insight: You must do work against electromagnetic force. This work equals the electrical energy dissipated.

Problem 2.2: A conducting rod rotates about one end in a uniform magnetic field perpendicular to plane. Does the rod experience any magnetic force?

Solution

Answer: Yes, the rod experiences a torque opposing its rotation.

Explanation:

  1. As rod rotates, flux through sector swept increases
  2. Induced EMF: $\mathcal{E} = \frac{1}{2}B\omega L^2$ (motional EMF)
  3. If circuit is complete, current flows: $I = \frac{\mathcal{E}}{R}$
  4. Force on each element $dl$ at distance $r$: $dF = BI \cdot dl$
  5. Torque opposes rotation (by Lenz’s law)
  6. Total torque: $\tau = \int r \cdot dF$ (retarding torque)

Without external torque: The rod will decelerate. With constant external torque: Steady state reached when input power = dissipated power.

Level 3: JEE Advanced (Challenging)

Problem 3.1: A square metallic frame falls vertically through a horizontal magnetic field. The field exists only in a limited region. Describe the motion of the frame as it: (a) Enters the field region (b) Is completely inside the field (c) Exits the field region

Solution

(a) Entering the field:

  • Top edge enters field → Flux through frame increases
  • By Lenz’s law, induced current opposes increase
  • Force on top edge (in field): Upward (opposes entry)
  • Frame decelerates (a < g)

(b) Completely inside:

  • Uniform field, no change in flux
  • No induced current, no induced EMF
  • Only gravity acts
  • Frame accelerates with a = g (free fall)

(c) Exiting the field:

  • Bottom edge exits field → Flux through frame decreases
  • By Lenz’s law, induced current opposes decrease
  • Force on bottom edge (still in field): Upward (opposes exit)
  • Frame decelerates again (a < g)

Motion graph:

Velocity
   ^
   |     /----\
   |    /      \
   |   /        \
   |  /          \
   |--------------->
   Enter  Inside  Exit  Time

The frame speeds up in the middle region and slows down while entering/exiting.

Problem 3.2: A conducting disc rotates in a perpendicular magnetic field. A circuit is connected between the center and rim. Explain the torque experienced using Lenz’s law and energy conservation.

Solution

Given: Disc of radius R rotates with angular velocity ω in field B (perpendicular to disc).

Analysis:

EMF generation:

  • Radial elements move in magnetic field
  • Motional EMF: $\mathcal{E} = \frac{1}{2}B\omega R^2$

Current flow:

  • If external resistance R is connected: $I = \frac{\mathcal{E}}{R_{total}}$
  • Current flows radially (center to rim or vice versa)

Lenz’s Law application:

  1. As disc rotates, imagine flux through sectors increasing
  2. Induced current opposes this rotation
  3. Force on radial current elements: Perpendicular to radius, opposing rotation
  4. Net torque: $\tau = -\frac{B^2\omega R^4}{2R_{total}}$ (retarding)

Energy conservation:

  • Mechanical work done against torque: $P_{mech} = \tau \cdot \omega$
  • Electrical power dissipated: $P_{elec} = I^2 R = \frac{\mathcal{E}^2}{R}$
  • By energy conservation: $P_{mech} = P_{elec}$ ✓

Key insight: The negative sign (Lenz’s law) ensures energy is conserved. The disc can’t spontaneously speed up and generate energy.

Lenz’s Law vs Faraday’s Law

AspectFaraday’s LawLenz’s Law
What it tellsMagnitude of induced EMFDirection of induced EMF/current
Formula$\|\mathcal{E}\| = N\frac{d\Phi_B}{dt}$Negative sign in complete formula
BasisExperimental observationConservation of energy
Use in JEECalculate EMF valueFind current direction, force direction

Applications of Lenz’s Law

  1. Electromagnetic Braking: Trains, roller coasters (safe, no wear)
  2. Eddy Current Damping: Galvanometer needles, weighing balances
  3. Induction Cooktops: Induced currents heat cookware
  4. Metal Detectors: Detect opposition from induced currents in metal
  5. Shock Absorbers: Some use electromagnetic damping
  6. Speedometers: Old cars used eddy current drag

Connection to Other Chapters

Key Takeaways

✓ Induced current always opposes the change causing it ✓ This opposition is a manifestation of energy conservation ✓ Lenz’s law gives direction, Faraday’s law gives magnitude ✓ Approach → Repel; Recede → Attract (for magnets) ✓ Moving conductors experience opposing forces (must do work) ✓ The negative sign in Faraday’s law represents Lenz’s law

Quick Decision Tree for Current Direction

Is flux increasing?
├─ YES → Induced field opposes external field
│         → Use RH rule to find current
└─ NO (decreasing) → Induced field supports external field
                    → Use RH rule to find current

Formula Summary

Complete Faraday’s Law (with Lenz):

$$\mathcal{E} = -N\frac{d\Phi_B}{dt}$$

Interpretation:

  • Magnitude: $|\mathcal{E}| = N\left|\frac{d\Phi_B}{dt}\right|$
  • Direction: Negative sign → Opposes change (Lenz’s law)

Energy Conservation:

$$\text{Work done against induced force} = \text{Electrical energy produced}$$

Next Topic: Motional EMF - EMF in moving conductors and force analysis