Lenz's Law Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Lenz's Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The direction of an induced current is always such that it opposes the change in magnetic flux that produced it.

Nature resists change — when you push a magnet into a coil, the coil creates its own magnetic field that pushes back.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Lenz's Law starts by naming the source, the object affected, and how the field or potential changes through space.

Common stuck point: Students often know a formula related to lenz's law but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I using a field or potential to explain how one object influences another across space?

Worked Examples

Example 1

easy
A north pole of a magnet is pushed toward a coil. According to Lenz's law, what pole does the coil's nearest face become? In which direction does the induced current flow (viewed from the magnet's side)?

Answer

Coil face becomes north pole; current flows counterclockwise (from magnet’s view)\text{Coil face becomes north pole; current flows counterclockwise (from magnet's view)}

First step

1
Lenz's law states the induced current opposes the change that caused it.

Full solution

  1. 2
    The approaching north pole increases the flux through the coil. To oppose this increase, the coil must create a magnetic field that repels the magnet.
  2. 3
    The nearest face of the coil becomes a north pole (repelling the incoming north pole), so the current flows counterclockwise when viewed from the magnet's side.
Lenz's law is a consequence of energy conservation. The induced current always creates effects that oppose the change in flux, requiring work to be done to maintain the change.

Example 2

medium
A circular loop is in a magnetic field pointing into the page. The field strength decreases. According to Lenz's law, in which direction does the induced current flow?

Example 3

medium
A loop has flux Φ(t)=(0.4 Wb)cos⁡(10t)\Phi(t) = (0.4\text{ Wb})\cos(10t). At t=0t = 0, is the induced EMF zero, maximum positive, or maximum negative?

Example 4

hard
A loop of resistance 2 Ω2\,\Omega has flux changing such that ∣dΦ/dt∣=6 V|d\Phi/dt| = 6\text{ V}. Find the power dissipated in the loop.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A conducting ring is dropped through a region of magnetic field. As it enters the field, the induced current creates an upward force on the ring. Explain this using Lenz's law.

Example 2

hard
A superconducting ring (zero resistance) is in a magnetic field of 0.5 T0.5 \text{ T}. The external field is suddenly turned off. What happens to the flux through the ring, and why?

Example 3

easy
What does Lenz's law tell you about an induced current?

Example 4

easy
Push a magnet's north pole toward a coil. What pole does the coil's near face become?

Example 5

easy
Pull a magnet's north pole away from a coil. What pole does the coil's near face become?

Example 6

easy
Does Lenz's law oppose the magnetic field, or the change in flux?

Example 7

easy
Lenz's law is a consequence of which conservation principle?

Example 8

easy
If flux through a loop increases, the induced current creates flux in which direction inside the loop?

Example 9

easy
Lenz's law gives the direction; which law gives the magnitude of the EMF?

Example 10

easy
A magnet falls through a vertical copper pipe. Does it fall faster or slower than free fall?

Example 11

medium
A loop in the page has flux out of the page increasing. Which way does the induced current flow?

Example 12

medium
A loop in the page has flux out of the page decreasing. Which way does the induced current flow?

Example 13

medium
A conducting loop moves toward a region of stronger field. Does the induced current oppose or aid its motion?

Example 14

medium
When you push a magnet into a coil, do you do positive or negative work, and where does the energy go?

Example 15

medium
A loop with flux into the page is increasing. Induced current direction?

Example 16

medium
A bar magnet is dropped through a coil connected to a resistor. Describe the kinetic energy outcome.

Example 17

challenge
A circular loop lies flat; a magnet's north pole approaches from above. State the induced current direction (viewed from above) and the resulting force on the magnet.

Example 18

challenge
A square loop exits a field region (field into page) moving right. State the induced current direction and the force on the loop.

Example 19

challenge
A coil sits in an oscillating field B(t)=B0sin⁡(ωt)B(t) = B_0\sin(\omega t). Describe how the induced current direction behaves over one cycle.

Example 20

medium
A loop with flux into the page is decreasing. Find the induced current direction.

Example 21

medium
A conducting loop moves away from a region of strong field. Does the induced force oppose or aid its motion?

Example 22

medium
A transformer's core flux oscillates. Why does the secondary current alternate direction?

Example 23

easy
A south pole of a magnet is pushed toward a coil. Which pole does the near face of the coil become?

Example 24

easy
A south pole approaches a loop from above. As seen from above, in which direction does the induced current flow?

Example 25

easy
A north pole is moved away from a coil. The induced current's resulting magnetic effect on the magnet is to attract or repel?

Example 26

medium
A horizontal circular loop sits with its plane perpendicular to a uniform vertical magnetic field BB pointing up. BB is steadily decreased. From above, in which direction does the induced current flow?

Example 27

medium
A loop is being pulled out of a field region (field into the page) to the right. State the direction of the induced current.

Example 28

medium
A loop's area increases while the perpendicular field BB (out of the page) stays constant. State the direction of the induced current.

Example 29

medium
Two coaxial coils sit side-by-side. The current in coil 1 is steadily increasing in the clockwise direction (viewed from coil 2). What direction does the induced current in coil 2 flow (viewed from coil 2)?

Example 30

medium
A loop sits in a field directed into the page. The field magnitude doubles in 0.1 s0.1\text{ s}. Does the induced current oppose or aid the original field inside the loop?

Example 31

medium
A magnet falls through a horizontal aluminum (non-magnetic but conductive) sheet. Why does the magnet feel a drag, even though aluminum is not magnetic?

Example 32

medium
A loop carrying a clockwise current sits in a region with no external field. Will the loop spontaneously continue to carry current? Why or why not?

Example 33

hard
A square loop of side 0.2 m0.2\text{ m} enters a region of field B=0.5 TB = 0.5\text{ T} (into page) at v=2 m/sv = 2\text{ m/s}. Resistance of the loop is 0.1 Ω0.1\,\Omega. Find the magnitude of the induced current as the loop enters.

Example 34

hard
Continuing the previous setup, find the magnitude and direction of the force needed to push the loop into the field at constant 2 m/s2\text{ m/s}.

Example 35

hard
A loop's flux is described by Φ(t)=(3t2−2t) Wb\Phi(t) = (3t^2 - 2t)\text{ Wb} for tt in seconds. Find the magnitude of the induced EMF at t=2 st = 2\text{ s}.

Example 36

hard
A circular loop of radius 0.1 m0.1\text{ m} has its plane perpendicular to a field BB that decreases uniformly from 0.4 T0.4\text{ T} to 0.1 T0.1\text{ T} in 0.2 s0.2\text{ s}. Find the induced EMF.

Example 37

hard
A rectangular loop is rotating about a horizontal axis at angular speed ω\omega in a horizontal uniform field BB. At the instant the loop's plane is parallel to BB, the EMF is at its ____.

Example 38

hard
Why do solid metal cores in transformers have laminations (thin sheets) rather than being solid blocks?

Example 39

hard
A long solenoid carrying increasing current is wrapped around a metal rod. State the direction of the induced current in the rod relative to the solenoid current.

Example 40

challenge
A metal disk rotates in a uniform magnetic field perpendicular to its face. Why does it experience a drag torque (eddy-current braking)?

Example 41

challenge
A square loop (0.1 m0.1\text{ m} side, R=0.2 ΩR = 0.2\,\Omega) is in a uniform B=0.5 TB = 0.5\text{ T} field into the page. The field is turned off uniformly in 0.05 s0.05\text{ s}. Find the magnitude and direction of the induced current.

Example 42

challenge
A superconducting ring (zero resistance) initially has flux Φ0\Phi_0 through it. The external field is then changed. What happens to the total flux through the ring?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

faradays lawelectromagnetic induction