Section 5.5: Lenz’s Law
Lenz’s Law states that the direction of an induced current or emf is such that it opposes the change in magnetic flux that produced it. This ensures the conservation of energy.
- Mathematical Expression: \[ \mathcal{E} = -\frac{d\Phi_B}{dt} \] The negative sign indicates the opposition to flux change.
- It explains why the induced current in a loop resists motion that changes the magnetic flux.
- Applications include electromagnetic braking, generators, and transformers.
Example: Induced Current Direction
A bar magnet is pushed into a coil. Determine the direction of the induced current in the coil.
The induced current will produce a magnetic field opposing the motion of the magnet entering the coil, i.e., opposing the increase in magnetic flux through the coil.
Practice Problems
- A coil experiences a decreasing magnetic flux. What is the direction of induced current?
- Explain why Lenz’s Law is a consequence of energy conservation.
- A magnet is pulled out of a coil at constant speed. Sketch the induced current as a function of time.
- Describe how Lenz’s Law is applied in electromagnetic braking.
- A solenoid experiences an increasing flux. Calculate the induced emf if the rate of flux change is 0.02 Wb/s and the solenoid has 50 turns.