Faraday's and Lenz's Laws
Induced EMF, motional EMF and eddy currents. (Physics › Electromagnetic Induction and Alternating Currents, NEET UG syllabus.)
What is Faraday's and Lenz's Laws?
The phenomenon of production of induced electromotive force (EMF) and current in a circuit due to a change in magnetic flux linked with it.
Key formula / rule: Faraday's Law of Electromagnetic Induction
Key points
- State and explain Faraday's Law of Electromagnetic Induction.
- Apply Lenz's Law to determine the direction of induced current/EMF.
- Calculate induced EMF given the rate of change of magnetic flux.
- Derive and apply the formula for motional EMF (E = Blv).
Common exam trap
Forgetting the negative sign in Faraday's Law or misinterpreting its meaning.
Definitions
- Term
Electromagnetic Induction
- Meaning
The phenomenon of production of induced electromotive force (EMF) and current in a circuit due to a change in magnetic flux linked with it.
- Term
Magnetic Flux (Φ)
- Meaning
A measure of the total number of magnetic field lines passing through a given area. It is the product of the magnetic field strength perpendicular to the area and the area itself. Unit: Weber (Wb).
- Term
Faraday's Law
- Meaning
States that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit.
- Term
Lenz's Law
- Meaning
States that the direction of the induced current or EMF is such that it opposes the cause producing it (i.e., the change in magnetic flux).
- Term
Motional EMF
- Meaning
The electromotive force induced across a conductor when it moves in a magnetic field, resulting from the Lorentz force on the charge carriers.
- Term
Eddy Currents
- Meaning
Circulating currents induced in bulk conductors when they are subjected to changing magnetic flux. They flow in closed loops within the material.
Learning objectives
State and explain Faraday's Law of Electromagnetic Induction.
Apply Lenz's Law to determine the direction of induced current/EMF.
Calculate induced EMF given the rate of change of magnetic flux.
Derive and apply the formula for motional EMF (E = Blv).
Describe eddy currents, their causes, effects, and applications.
Solve problems involving changing magnetic flux, motional EMF, and eddy currents.
Formulae
- Name
Faraday's Law of Electromagnetic Induction
- Note
E is induced EMF, Φ is magnetic flux, t is time. The negative sign indicates the direction as per Lenz's Law.
- Expression
E = -dΦ/dt
- Name
Magnetic Flux
- Note
For a uniform magnetic field B passing through a plane area A at an angle θ with the normal to the area, Φ = BAcosθ.
- Expression
Φ = ∫B⋅dA
- Name
Motional EMF
- Note
For a conductor of length 'l' moving with velocity 'v' perpendicular to a uniform magnetic field 'B'.
- Expression
E = Blv
- Name
Induced Current
- Note
Where R is the resistance of the circuit.
- Expression
I = E/R
Prerequisites
Basic understanding of magnetic fields and magnetic field lines.
Concept of magnetic flux.
Lorentz force on moving charges in a magnetic field.
Basic calculus (differentiation).
Principle of conservation of energy.
Common mistakes
Forgetting the negative sign in Faraday's Law or misinterpreting its meaning.
Incorrectly applying Lenz's Law to determine the direction of induced current.
Confusing magnetic flux with magnetic field strength.
Not understanding that motional EMF is a specific case of Faraday's Law.
Ignoring the effects of eddy currents in practical applications or problems.
Keywords
Faraday's Law
Lenz's Law
Electromagnetic Induction
Magnetic Flux
Induced EMF
Motional EMF
Eddy Currents
Conservation of Energy
Lorentz Force
Practice preview
According to Lenz's law, the direction of the induced current in a circuit is such that it:…
easy
A straight conductor of length L moves with a uniform velocity v perpendicular to a uniform magnetic field B. The motional EMF induced across its ends is given by:…
easy
A coil has 100 turns and a cross-sectional area of 0.01 m^2. The magnetic field passing perpendicularly through the coil changes from 0.5 T to 0.1 T in 0.2 seconds. What is the magnitude of the induced EMF in the coil?…
medium