23.3 Motional Emf

Electromagnetic induction is a fascinating phenomenon where changing magnetic fields create electric currents. Motional EMF, a specific type, occurs when conductors move through magnetic fields. This process is crucial for many everyday devices, from electric guitars to generators.

Understanding motional EMF involves key concepts like Faraday's law and Lenz's law. These principles explain how moving conductors in magnetic fields generate electricity, and why induced currents flow in specific directions. This knowledge is essential for grasping the workings of various electrical machines.

Motional EMF

Electromagnetic Induction and Motional EMF

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• Electromagnetic induction: process of generating electric current by changing magnetic field
• Motional emf ($\mathcal{E}$) generated when a conductor moves through a magnetic field (a specific form of electromagnetic induction)
  • Formula: $\mathcal{E} = Blv$
    • $B$ magnetic field strength (also known as magnetic flux density)
    • $l$ length of the conductor
    • $v$ velocity of the conductor perpendicular to the magnetic field
  • Examples: electric guitar pickups, electric generators
• Faraday's law: relates the induced electromotive force (emf) to the rate of change of magnetic flux
• Flux: measure of the total magnetic field passing through a given area

Emf, force, and work calculations

• Force on a current-carrying conductor in a magnetic field: [object Object],[object Object]
  • $I$ current in the conductor
  • $\theta$ angle between the current direction and the magnetic field
  • Maximum force occurs when current is perpendicular to magnetic field ($\theta = 90^\circ$)
  • Examples: electric motors, loudspeakers
• Work done by magnetic force on a moving conductor: [object Object],[object Object]
  • $d$ displacement of the conductor in the direction of the force
  • Work done depends on the force and the distance the conductor moves
  • Examples: electric generators, transformers

Generation of motional emf

• When a conductor moves through a magnetic field, free electrons in the conductor experience a force due to the magnetic field
  • This force causes electrons to move, creating an induced current in the conductor
  • Induced emf depends on velocity of conductor, strength of magnetic field, and length of conductor in the magnetic field
  • Examples: dynamos, alternators
• Direction of induced current determined by Lenz's law
  • Induced current creates a magnetic field that opposes the change in magnetic flux caused by the conductor's motion
  • Examples: eddy current brakes, induction cooktops

Lenz's law in induced currents

• Lenz's law states that direction of induced current in a conductor is such that it opposes the change that caused it
  • In motional emf, induced current creates a magnetic field that opposes the change in magnetic flux caused by the conductor's motion
• To determine direction of induced current:
  1. Use right-hand rule to find direction of magnetic force on the conductor
  2. Induced current will flow in direction opposite to the magnetic force
• Examples:
  • Electromagnetic braking in trains
  • Back emf in electric motors