Faraday's law of induction

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Stokes'_Theorem

Faraday's law of induction

Faraday's law of induction is a fundamental principle of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction.

History

The law is named after Michael Faraday, who conducted extensive research on electromagnetic induction in the early 19th century. Faraday's experiments demonstrated that a changing magnetic field within a closed loop of wire induces an electric current in the wire.

Mathematical Formulation

Faraday's law of induction can be mathematically expressed as:

\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]

where:

• \(\mathcal{E}\) is the induced EMF,
• \(\Phi_B\) is the magnetic flux through the circuit,
• \(t\) is time.

The negative sign in the equation represents Lenz's law, which states that the direction of the induced EMF and the resulting current will oppose the change in magnetic flux that produced them.

Applications

Faraday's law of induction is the principle behind many electrical devices and technologies, including:

• Electric generators
• Transformers
• Induction cooktops
• Magnetic flow meters

Related Concepts

• Lenz's law
• Maxwell's equations
• Electromagnetic induction
• Magnetic flux
• Electromotive force

See Also

• Michael Faraday
• Electromagnetism
• Electric circuit
• Magnetic field
• Electric current