What does Faraday's law state?
2 Answers
Faraday's law of electromagnetic induction states that the electromotive force (EMF) induced in a circuit is directly proportional to the rate of change of magnetic flux through that circuit. In simpler terms, when the magnetic field around a conductor changes, it induces an electric current in the conductor. This principle is fundamental to the operation of many electrical devices, such as generators and transformers. The law can be expressed mathematically as:
\[
\text{EMF} = -\frac{d\Phi_B}{dt}
\]
where \(\Phi_B\) is the magnetic flux, and the negative sign indicates the direction of the induced EMF (as described by Lenz's law).
\[
\text{EMF} = -\frac{d\Phi_B}{dt}
\]
where \(\Phi_B\) is the magnetic flux, and the negative sign indicates the direction of the induced EMF (as described by Lenz's law).
Faraday's Law of Electromagnetic Induction is a fundamental principle in electromagnetism. It states that a change in the magnetic field within a closed loop induces an electromotive force (EMF) in the wire making up the loop. Here's a more detailed breakdown:
1. **Induced EMF**: The law quantifies the induced EMF (\( \mathcal{E} \)) in a circuit as proportional to the rate of change of the magnetic flux (\( \Phi_B \)) through the circuit. Mathematically, it is expressed as:
\[
\mathcal{E} = -\frac{d\Phi_B}{dt}
\]
where \( \mathcal{E} \) is the induced EMF, \( \frac{d\Phi_B}{dt} \) is the rate of change of the magnetic flux, and the negative sign represents Lenz's Law, which indicates the direction of the induced EMF opposes the change in flux.
2. **Magnetic Flux**: Magnetic flux (\( \Phi_B \)) through a surface is defined as the product of the magnetic field (\( B \)) and the area (\( A \)) of the surface, and the cosine of the angle (\( \theta \)) between the field lines and the normal to the surface:
\[
\Phi_B = B \cdot A \cdot \cos(\theta)
\]
3. **Lenz's Law**: The negative sign in Faraday's Law is a reflection of Lenz's Law, which states that the direction of the induced EMF is such that it creates a current whose magnetic field opposes the change in the original magnetic field.
Faraday's Law is fundamental to the operation of many electrical devices, such as transformers, electric generators, and inductors. It highlights the relationship between electricity and magnetism, showing how changing magnetic fields can produce electric currents.
1. **Induced EMF**: The law quantifies the induced EMF (\( \mathcal{E} \)) in a circuit as proportional to the rate of change of the magnetic flux (\( \Phi_B \)) through the circuit. Mathematically, it is expressed as:
\[
\mathcal{E} = -\frac{d\Phi_B}{dt}
\]
where \( \mathcal{E} \) is the induced EMF, \( \frac{d\Phi_B}{dt} \) is the rate of change of the magnetic flux, and the negative sign represents Lenz's Law, which indicates the direction of the induced EMF opposes the change in flux.
2. **Magnetic Flux**: Magnetic flux (\( \Phi_B \)) through a surface is defined as the product of the magnetic field (\( B \)) and the area (\( A \)) of the surface, and the cosine of the angle (\( \theta \)) between the field lines and the normal to the surface:
\[
\Phi_B = B \cdot A \cdot \cos(\theta)
\]
3. **Lenz's Law**: The negative sign in Faraday's Law is a reflection of Lenz's Law, which states that the direction of the induced EMF is such that it creates a current whose magnetic field opposes the change in the original magnetic field.
Faraday's Law is fundamental to the operation of many electrical devices, such as transformers, electric generators, and inductors. It highlights the relationship between electricity and magnetism, showing how changing magnetic fields can produce electric currents.