Faraday’s Law of Induction

  • Joseph Henry and Michael Faraday had independently discovered the phenomenon of electromagnetic induction in the early 19th century.
  • Electromagnetic induction occurs when a conductor cuts across magnetic field lines.
  • Faraday’s law of electromagnetic induction states that the induced electromotive force (emf) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
  • The induced emf (e) is given by the equation: e = -N(dΦ/dt), where N is the number of turns in the circuit coil and (dΦ/dt) is the rate of change of magnetic flux.
  • The negative sign indicates that the induced emf opposes the change in magnetic flux.

Mutual and Self-Inductance

  • Mutual inductance occurs when there are two or more coils in close proximity.
  • Self-inductance occurs when a single coil produces an induced emf in itself.
  • Both mutual and self-inductance are quantified by the property called inductance (L).
  • The unit of inductance is the Henry (H).
  • The inductance of a coil depends on factors like the number of turns, the geometry of the coil, and the presence of any core material.

Mutual Inductance and Faraday’s Law

  • Mutual inductance (M) is a measure of the extent to which a change in current in one coil induces an emf in an adjacent coil.
  • The mutual inductance between two coils is given by the equation: M = k√(L₁L₂), where k is the coupling coefficient, and L₁ and L₂ are the inductances of the coils.
  • Faraday’s law of electromagnetic induction can also be expressed in terms of mutual inductance: e₁ = -M(dI₂/dt), where e₁ is the induced emf in coil 1, and dI₂/dt is the rate of change of current in coil 2.

Self-Inductance and Faraday’s Law

  • Self-inductance occurs when a change in current in a coil induces an emf in the same coil.
  • The induced emf in a coil due to self-inductance is given by the equation: e = -L(dI/dt), where L is the self-inductance of the coil.
  • The negative sign indicates that the induced emf opposes the change in current.
  • Self-inductance depends on the geometry of the coil and the presence of any core material.

Induced EMF and Magnetic Field

  • According to Faraday’s law, the induced emf is directly proportional to the rate of change of magnetic flux.
  • Magnetic flux (Φ) through a loop of area (A) is given by the equation: Φ = B⊥A, where B⊥ is the magnetic field perpendicular to the area.
  • Therefore, we can rewrite Faraday’s law as: e = -N(d(B⊥A)/dt).
  • Magnetic field lines that are parallel or perpendicular to the area contribute to the magnetic flux, while those at other angles do not.

Lenz’s Law

  • Lenz’s law states that the direction of the induced current (or emf) is such that it opposes the change producing it.
  • This law is a consequence of the conservation of energy.
  • Lenz’s law helps us determine the direction of induced currents in circuits.
  • When a magnetic field through a loop increases, the induced current creates a magnetic field that opposes the increase.
  • When a magnetic field through a loop decreases, the induced current creates a magnetic field that opposes the decrease.

Examples of Faraday’s Law and Lenz’s Law

  • Example 1: A coil with 200 turns and an inductance of 0.05 H is subjected to a changing magnetic field with a rate of change of 50 T/s. Calculate the induced emf in the coil.
  • Example 2: A bar magnet is moved towards a coil. Determine the direction of the induced current in the coil, according to Lenz’s law.
  • Example 3: A solenoid coil is connected to a battery and a switch. When the switch is closed, the magnetic flux through the solenoid increases. Determine the direction of the induced current in the solenoid.

Applications of Faraday’s Law of Induction

  • Transformers: Transformers work on the principle of electromagnetic induction and are used to step-up or step-down voltage levels.
  • Generators: Electric generators convert mechanical energy into electrical energy through the process of electromagnetic induction.
  • Inductive Charging: Inductive charging is used to wirelessly recharge devices like smartphones and electric vehicles.
  • Magnetic Flow Meters: Magnetic flow meters measure the flow rate of conductive fluids using Faraday’s law of induction.

Summary

  • Faraday’s law of electromagnetic induction states that the induced emf in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
  • Mutual inductance occurs when there are two or more coils in close proximity, while self-inductance occurs when a single coil produces an induced emf in itself.
  • Lenz’s law states that the induced current opposes the change producing it.
  • Faraday’s law and Lenz’s law have various applications in transformers, generators, inductive charging, and magnetic flow meters.
  1. Faraday’s Law of Induction
  • Joseph Henry and Michael Faraday discovered electromagnetic induction.
  • Induction occurs when a conductor cuts across magnetic field lines.
  • Faraday’s law states that induced emf is proportional to the rate of change of magnetic flux through a circuit.
  • Induced emf (e) = -N(dΦ/dt), where N is the number of coil turns.
  • The negative sign indicates the induced emf opposition to the change.
  1. Mutual and Self-Inductance
  • Mutual inductance occurs between coils in close proximity.
  • Self-inductance occurs when a coil induces emf in itself.
  • Both are quantified by inductance (L) measured in Henry (H).
  • Inductance depends on factors like number of turns and coil geometry.
  • Inductance is also affected by the presence of core material.
  1. Mutual Inductance and Faraday’s Law
  • Mutual inductance (M) measures the extent of induced emf between coils.
  • M = k√(L₁L₂), where k is the coupling coefficient.
  • Faraday’s law in terms of mutual inductance: e₁ = -M(dI₂/dt).
  • e₁ is the induced emf in coil 1 and dI₂/dt is the rate of change of current in coil 2.
  • Induced emf opposes changes in magnetic flux and current.
  1. Self-Inductance and Faraday’s Law
  • Self-inductance occurs when a coil induces emf in itself.
  • The induced emf in a coil is given by: e = -L(dI/dt).
  • e is the induced emf, L is the self-inductance of the coil.
  • The negative sign indicates the induced emf opposes the change in current.
  • Self-inductance depends on coil geometry and core material.
  1. Induced EMF and Magnetic Field
  • Induced emf is directly proportional to the rate of change of magnetic flux.
  • Magnetic flux (Φ) through a loop of area (A) = B⊥A.
  • Faraday’s law formula can be rewritten as: e = -N(d(B⊥A)/dt).
  • Magnetic flux is contributed by magnetic field lines parallel or perpendicular to the area.
  • Magnetic field lines at other angles do not contribute to the flux.
  1. Lenz’s Law
  • Lenz’s law states that induced current opposes the change producing it.
  • It is a consequence of energy conservation.
  • Lenz’s law helps determine the direction of induced currents.
  • When the magnetic field through a loop increases, the induced current creates a field opposing the increase.
  • When the magnetic field decreases, the induced current opposes the decrease.
  1. Examples of Faraday’s Law and Lenz’s Law
  • Example 1: A coil with 200 turns and inductance 0.05 H experiences a changing magnetic field with a rate of change of 50 T/s. Calculate the induced emf in the coil.
  • Example 2: A bar magnet is moved towards a coil. Determine the direction of the induced current in the coil according to Lenz’s law.
  • Example 3: A solenoid coil connected to a battery and a switch. When the switch is closed, the magnetic flux through the solenoid increases. Determine the direction of the induced current in the solenoid.
  1. Applications of Faraday’s Law of Induction
  • Transformers: Step-up/Step-down voltage levels.
  • Generators: Convert mechanical energy to electrical energy through induction.
  • Inductive Charging: Wireless charging for smartphones and electric vehicles.
  • Magnetic Flow Meters: Measure flow rate of conductive fluids based on Faraday’s law.
  1. Summary
  • Faraday’s law states induced emf is proportional to the rate of change of magnetic flux.
  • Mutual inductance occurs between close coils, self-inductance occurs within a coil.
  • Inductance depends on turns, geometry, and core material.
  • Faraday’s law in terms of mutual inductance: e₁ = -M(dI₂/dt).
  • Induced emf opposes magnetic flux and current change.
  1. Summary (contd.)
  • Self-inductance formula: e = -L(dI/dt).
  • Induced emf opposes current change.
  • Lenz’s law states induced current opposes the change.
  • Applications include transformers, generators, inductive charging, and magnetic flow meters.
  • Understanding Faraday’s and Lenz’s laws is crucial for various aspects of electromagnetism.

Applications of Faraday’s Law of Induction (contd.)

  • Electromagnetic Brakes: Faraday’s law is used in electromagnetic brakes to convert electrical energy into mechanical energy to slow down or stop moving objects.
  • Eddy Currents: When a conductor moves through a magnetic field, eddy currents are induced, which resist the motion of the conductor and produce heat.
  • Magnetic Levitation: Faraday’s law is utilized in magnetic levitation systems to suspend objects in mid-air using the repulsion of magnetic fields.
  • Induction Heating: Induction heating is widely used in industry to heat metals and other conductive materials through the process of electromagnetic induction.
  • Magnetic Resonance Imaging (MRI): MRI machines use Faraday’s law to generate magnetic fields and measure the response of the body’s atoms to these fields, creating detailed images of internal body structures.
  • Wireless Power Transfer: Inductive coupling is used in wireless power transfer systems to transmit electrical energy between coils without the need for direct electrical connections.

Faraday’s Law and Electrical Generators

  • Electric generators are devices that convert mechanical energy into electrical energy using Faraday’s law of electromagnetic induction.
  • A generator consists of a coil of wire rotating within a magnetic field.
  • When the coil rotates, the magnetic field through the coil changes, inducing an emf according to Faraday’s law.
  • This induced emf produces a current in the coil, which can be extracted as electrical energy.

Faraday’s Law and Transformers

  • Transformers are devices that alter the voltage level of an alternating current (AC) without changing its frequency.
  • Transformers work based on the principle of mutual induction between primary and secondary coils.
  • The changing current in the primary coil produces a changing magnetic field, which induces an emf in the secondary coil according to Faraday’s law.
  • The ratio of the number of turns in the primary and secondary coils determines the voltage ratio of the transformer.

Faraday’s Law and Magnetic Flow Meters

  • Magnetic flow meters are used to measure the flow rate of conductive fluids.
  • These meters utilize Faraday’s law of electromagnetic induction.
  • A magnetic field is applied perpendicular to the flow of the fluid, and electrodes detect the voltage induced by the fluid passing through the magnetic field.
  • The induced voltage is proportional to the velocity of the fluid, allowing for the measurement of flow rate.

Faraday’s Law and Inductive Sensors

  • Inductive sensors are used to detect the presence or absence of metallic objects.
  • These sensors work based on Faraday’s law of electromagnetic induction.
  • When a metallic object enters the sensing region of the inductive sensor, it induces eddy currents in the object, which in turn induce an emf in the sensing coil.
  • The change in the induced emf is detected and used to determine the presence or absence of the object.

Faraday’s Law and Coils in Circuits

  • Coils with inductance play a crucial role in electrical circuits.
  • When the current through a coil changes, an induced emf opposes the change according to Faraday’s law.
  • This phenomenon is utilized in devices like inductors and solenoids.
  • Inductors are passive components that store energy in the form of a magnetic field when current flows through them.
  • Solenoids are coils with an iron core that produce a strong magnetic field when current passes through them.

Faraday’s Law and AC Generators

  • AC generators, also known as alternators, are used to produce alternating current (AC) electrical energy.
  • They work based on Faraday’s law of electromagnetic induction.
  • AC generators consist of rotating coils within a magnetic field.
  • As the coils rotate, the magnetic field through them changes, inducing an alternating current in the coils.
  • This alternating current can be used to power various electrical devices.

Faraday’s Law and Eddy Current Brakes

  • Eddy current brakes are used to slow down or stop moving objects.
  • They work based on Faraday’s law and Lenz’s law.
  • As a conductor moves through a magnetic field, eddy currents are induced in the conductor, which create a magnetic field opposing the motion.
  • The magnetic field of the eddy currents interacts with the magnetic field of the brake, generating a resisting force that slows down the object.

Faraday’s Law and Magnetic Resonance Imaging (MRI)

  • Magnetic resonance imaging (MRI) is a medical imaging technique that uses strong magnetic fields and radio waves to create detailed images of the body’s internal structures.
  • MRI machines work based on Faraday’s law of electromagnetic induction.
  • The magnetic fields produced by the machine cause the body’s atoms to align with the magnetic field.
  • Small radio frequency signals are then applied, causing the atoms to resonate.
  • The resonance signals are detected and used to create the images.

Faraday’s Law and Inductive Charging

  • Inductive charging is a wireless charging technology that uses Faraday’s law of electromagnetic induction.
  • It is commonly used for charging smartphones, electric toothbrushes, and electric vehicles.
  • Inductive charging pads generate a magnetic field, which induces an emf in a receiving coil in the device to be charged.
  • The induced emf is then rectified and used to charge the device’s battery.

Recap

  • Faraday’s law of induction states that the induced electromotive force (emf) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
  • Mutual inductance occurs between two coils, while self-inductance occurs in a single coil.
  • Lenz’s law states that the induced current or emf in a circuit opposes the change producing it.
  • Faraday’s law and Lenz’s law have various applications, including transformers, generators, inductive charging, and magnetic flow meters.
  • Understanding Faraday’s law and its applications is essential for the study of electromagnetism.