What is called Faraday's law?
2 Answers
Faraday's law, often referred to as Faraday's law of electromagnetic induction, describes how a changing magnetic field can induce an electromotive force (EMF) in a conductor. Specifically, it states that the induced EMF in a closed loop is directly proportional to the rate of change of the magnetic flux through that loop. Mathematically, it can be expressed as:
\[
\mathcal{E} = -\frac{d\Phi_B}{dt}
\]
where \(\mathcal{E}\) is the induced EMF, \(\Phi_B\) is the magnetic flux, and \(\frac{d\Phi_B}{dt}\) is the rate of change of the magnetic flux. The negative sign indicates the direction of the induced EMF opposes the change in flux, a principle known as Lenz's law. Faraday's law is fundamental in understanding how generators and transformers work.
\[
\mathcal{E} = -\frac{d\Phi_B}{dt}
\]
where \(\mathcal{E}\) is the induced EMF, \(\Phi_B\) is the magnetic flux, and \(\frac{d\Phi_B}{dt}\) is the rate of change of the magnetic flux. The negative sign indicates the direction of the induced EMF opposes the change in flux, a principle known as Lenz's law. Faraday's law is fundamental in understanding how generators and transformers work.
Faraday's Law refers to two fundamental principles in electromagnetism discovered by Michael Faraday in the 19th century. These principles describe how electric currents are generated by changing magnetic fields and how magnetic fields are influenced by electric currents. Here’s a detailed look at each component:
### 1. Faraday's Law of Induction
**Statement:** Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed circuit is proportional to the rate of change of the magnetic flux through the circuit.
**Mathematical Expression:**
\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]
Where:
- \(\mathcal{E}\) is the induced EMF (voltage).
- \(\Phi_B\) is the magnetic flux through the circuit.
- \(t\) is time.
**Explanation:** Magnetic flux (\(\Phi_B\)) is the product of the magnetic field (\(B\)) and the area (\(A\)) through which the field lines pass, and it also depends on the angle (\(\theta\)) between the magnetic field and the perpendicular to the surface:
\[ \Phi_B = B \cdot A \cdot \cos(\theta) \]
When the magnetic flux through a loop or coil changes—due to a change in the magnetic field strength, the area of the loop, or the orientation of the loop—the induced EMF generates a current if the circuit is closed. The negative sign in the formula indicates Lenz's Law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.
### 2. Faraday's Law of Electrolysis
**Statement:** Faraday’s Law of Electrolysis quantifies the amount of substance transformed at an electrode during electrolysis. It states that the amount of chemical change produced at an electrode is directly proportional to the quantity of electric charge passed through the electrolyte.
**Mathematical Expression:**
\[ m = \frac{Q \cdot M}{n \cdot F} \]
Where:
- \(m\) is the mass of the substance transformed.
- \(Q\) is the total electric charge passed through the electrolyte.
- \(M\) is the molar mass of the substance.
- \(n\) is the number of electrons involved in the reaction.
- \(F\) is Faraday's constant (\(≈ 96485 \text{ C/mol}\)).
**Explanation:** Faraday's Law of Electrolysis relates the quantity of electricity (charge) passed through an electrolyte to the amount of substance deposited or dissolved at the electrodes. This law is foundational in electrochemistry and helps in calculating quantities of substances involved in electrochemical reactions.
### Applications and Importance
1. **Electromagnetic Induction:** Faraday’s Law of Induction is crucial in the design of electric generators, transformers, and inductors. It explains how electric currents can be generated from changing magnetic fields, which is a principle behind many electrical devices and power generation systems.
2. **Electrolysis:** Faraday’s Law of Electrolysis is used in electroplating, battery design, and chemical manufacturing processes, where control over the amount of substance produced or consumed is essential.
Overall, Faraday’s Laws form a cornerstone of electromagnetism and electrochemistry, providing fundamental insights into how electric and magnetic fields interact with matter.
### 1. Faraday's Law of Induction
**Statement:** Faraday's Law of Induction states that the electromotive force (EMF) induced in a closed circuit is proportional to the rate of change of the magnetic flux through the circuit.
**Mathematical Expression:**
\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]
Where:
- \(\mathcal{E}\) is the induced EMF (voltage).
- \(\Phi_B\) is the magnetic flux through the circuit.
- \(t\) is time.
**Explanation:** Magnetic flux (\(\Phi_B\)) is the product of the magnetic field (\(B\)) and the area (\(A\)) through which the field lines pass, and it also depends on the angle (\(\theta\)) between the magnetic field and the perpendicular to the surface:
\[ \Phi_B = B \cdot A \cdot \cos(\theta) \]
When the magnetic flux through a loop or coil changes—due to a change in the magnetic field strength, the area of the loop, or the orientation of the loop—the induced EMF generates a current if the circuit is closed. The negative sign in the formula indicates Lenz's Law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.
### 2. Faraday's Law of Electrolysis
**Statement:** Faraday’s Law of Electrolysis quantifies the amount of substance transformed at an electrode during electrolysis. It states that the amount of chemical change produced at an electrode is directly proportional to the quantity of electric charge passed through the electrolyte.
**Mathematical Expression:**
\[ m = \frac{Q \cdot M}{n \cdot F} \]
Where:
- \(m\) is the mass of the substance transformed.
- \(Q\) is the total electric charge passed through the electrolyte.
- \(M\) is the molar mass of the substance.
- \(n\) is the number of electrons involved in the reaction.
- \(F\) is Faraday's constant (\(≈ 96485 \text{ C/mol}\)).
**Explanation:** Faraday's Law of Electrolysis relates the quantity of electricity (charge) passed through an electrolyte to the amount of substance deposited or dissolved at the electrodes. This law is foundational in electrochemistry and helps in calculating quantities of substances involved in electrochemical reactions.
### Applications and Importance
1. **Electromagnetic Induction:** Faraday’s Law of Induction is crucial in the design of electric generators, transformers, and inductors. It explains how electric currents can be generated from changing magnetic fields, which is a principle behind many electrical devices and power generation systems.
2. **Electrolysis:** Faraday’s Law of Electrolysis is used in electroplating, battery design, and chemical manufacturing processes, where control over the amount of substance produced or consumed is essential.
Overall, Faraday’s Laws form a cornerstone of electromagnetism and electrochemistry, providing fundamental insights into how electric and magnetic fields interact with matter.