Faraday's Law of Induction: Faraday's Law describes the relationship between magnitude of the electromotive force (emf), or voltage, induced (generated) in a conductor due to electromagnetic induction (changing magnetic fields). English scientist Michael Faraday first put forward this law in 1831. This law is crucial for explaining the operation of various electrical devices like generators, transformers, and motors.
Faraday’s Law of Electromagnetic Induction: Definition
Faraday's Law of Electromagnetic Induction states that the induced electromotive force (emf) in a closed loop is proportional to the rate of change of magnetic flux through the loop.
Mathematically, it is expressed as:
ε = - dΦB/dt
where:
→ ε is the induced emf.
→ ΦB is the magnetic flux through the loop, given by ΦB=BAcosθ
- B is the magnetic field strength.
- A is the area of the loop.
- θ is the angle between the area vector and the magnetic field.
The negative sign indicates the induced EMF opposes the change in magnetic flux.
In the case of a closely wound coil of N turns, the expression for the total induced emf is given by
ε = -N(dΦB/dt)
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Factors Affecting Induced EMF in a Circuit
The induced emf can be changed by varying the following factors:
- Magnetic Field Strength (B): Stronger the magnetic field, greater will be the flux change in the circuit. This will lead to a higher induced emf.
- Loop Area (A): Increasing the area of the loop will increase the magnetic flux for a given magnetic field strength, resulting in a higher induced emf.
- Angle (θ): The angle between the magnetic field and the normal to the loop's surface affects the magnetic flux. The induced emf is maximum when the magnetic field is perpendicular to the loop (for θ=0∘, cosθ=1) and zero when the magnetic field is parallel to the loop (for θ=90∘, cosθ=0).
- Number of Turns (N) in Coil: More the number of turns in the coil, greater will be the induced emf.
- Strength of Current in the Coil: A stronger current will create a stronger magnetic field within the loop, resulting in a higher induced emf.
Faraday’s Laws of Electromagnetic Induction
Faraday's Laws of Electromagnetic Induction consist of two principal laws which have been explained below:
1. Faraday's First Law of Electromagnetic Induction
This law states that whenever the magnetic flux associated with a coil changes, emf is induced in that coil. In simpler terms, a moving magnet or a changing current can induce a voltage in a nearby coil.
This is a qualitative law as it only indicates the existence of induced emf.
| Key Points: The direction of the induced emf depends on the direction of the change in the magnetic field. The magnitude of the induced emf is proportional to the rate of change of the magnetic field. |
2. Faraday's Second Law of Electromagnetic Induction
This law quantifies the relationship between the induced emf and the rate of change of magnetic flux. The magnitude of induced emf produced in the circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.
Mathematical expression:
ε = -dΦB/dt
| Key Points: This law emphasises that the induced emf is not just dependent on the change in the magnetic field but also on the amount of magnetic flux passing through the loop. More loops in a coil (larger area) will generally encompass more magnetic flux, leading to a larger induced emf. |
3. Lenz's Law
This law complements Faraday's Laws by specifying the direction of the induced current caused by the induced emf. It states that the direction of the induced current in a conductor is always such that it opposes the change in the magnetic field that produced it.
Lenz’s Law is named after the German physicist “Heinrich Friedrich Lenz”, who formulated it in 1834.
| Key Points: Lenz's Law helps determine the direction of the induced emf based on the direction of the change in the magnetic field. This law ensures energy conservation. The induced current and its magnetic field resist the change that caused them, creating a self-regulating system. |
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Applications of Faraday's Law
Faraday's law has numerous applications in various technologies:
- Generators: Generators convert mechanical energy into electrical energy. As a conductor (or a coil) rotates within a magnetic field, the changing magnetic flux induces an EMF, generating an electric current.
- Transformers: Transformers transfer electrical energy between circuits and change voltage levels. They use the principle of changing magnetic fields to step up or step down voltages in AC circuits.
- Electric Motors: They convert electrical energy into mechanical energy. They rely on the interaction between a changing magnetic field and current-carrying coils to produce torque and rotation.
- Induction Cooktop: An alternating current passes through a coil beneath the cooktop, creating a changing magnetic field that induces eddy currents in the metal pot, producing heat.
- Inductors: Inductors are electrical components that use Faraday's law to oppose changes in current by inducing a voltage in the opposite direction.
By understanding Faraday's law, we can explain and predict the behaviour of many electrical devices and systems that rely on the interaction between magnetism and electricity.
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