IB Physics Unit 11. Electromagnetic Induction: Notes

Understandings

➔ Electromotive force (emf)

➔ Magnetic flux and magnetic flux linkage

➔  Faraday’s law of induction

➔ Lenz’s law

Applications and skills

➔ Describing the production of an induced emf by a changing magnetic flux and within a uniform magnetic field

➔ Solving problems involving magnetic flux, magnetic flux linkage, and Faraday’s law

➔ Explaining Lenz’s law through the conservation of energy

Equations

➔ Flux: Φ = BA cosθ

➔  Faraday’s / Neumann’s equation: ε = –N (dΦ/dt)

➔ emf induced in moving rod: ε = Bvl

➔ in side of coil with N turns: ε = BvlN

11.1 Electromagnetic Induction

Electromagnetic induction: When an electric charge moves in a magnetic field, then a force acts on it. In a reverse sense, a movement or change in magnetic field relative to stationary charge gives raise to an electric current.

Induced emf (ε)

  • Definition: Potential difference generated by electromagnetic induction.

For a rod of length L moved with velocity v in a region of magnetic field B:

  • If ​the rod moves from left to right, and thus, its electrons move perpendicular to the magnetic field, they experience a downward force along the rod and an electric field is established.

  • Flow of electrons quickly stops due to electrostatic repulsion at the bottom, and thus, the current exists for a short period of time.

  • Without movement, emf is not induced.

  • Formula if the rod is moved connected to wires (the work done to separate electrons leads to an induced emf): ε = BvL.

Magnetic flux (Ф)

  • Definition: “Product of the magnitude of the normal component of magnetic field strength and area through which it passes.”

  • Intuitive picture: Number of magnetic field lines crossing a certain area.

  • Formula: Ф = BAcosθ, where A is the area and θ is the angle between the magnetic field strength direction and the direction normal to the loop area.

  • Units: weber (Wb)

FieldArea.png
  • Definition for a rod: “Product of magnitude and the rate at which the area swept out by the rod is changing” = ∆Ф/∆t.

FieldSmth.png
  • Magnetic flux linkage: Magnetic flux multiplied by the N turns in a loop. Ф = NBAcosθ.

  • Magnetic flux density: numerically equivalent to magnetic field strength.

    • Induced emf = magnetic flux density x rate of change of area =​ B∆A/∆t.

Faraday’s Law

  • Definition: “Induced emf is equal to the negative rate of change of magnetic flux linkage.”

    • Negative sign exists due to Lenz’s law (see below).​

  • Formula: ε = -N∆Ф/∆t.

Magnetic field away from viewerwiremagneticfield.png

Coil of area A with N turns

Example of Faraday’s Law:

A coiled wire is moving into a magnetic field.

The induced current should create a magnetic field in a direction opposed to the existing field (in this case, opposing “away from”, therefore, towards the viewer)

  • Rod (perpendicular to field): in time ∆t, a rod of length L will move a distance s = v∆t, cutting magnetic field lines as it moves in the magnetic field. A = Ls

    • Formula: ​∆Ф = ∆BAcos0º = ∆BA = ∆BLs = BLv∆t, and hence, ε = BvL.

Lenz’s Law

  • Definition: “The induced emf will be in such a direction to oppose the change in the magnetic flux that crea

  • ted the current​”. It is equivalent to energy conservation.

  • Work done by magnetic forces that arises due to current is dissipated as thermal energy.

Examples:

  • Rod: Force in the rod must oppose 

    • Use left-hand rule twice: Firstly to find the direction of the current in the loop. Secondly, to find the force induced on the rod due to the current the motion. Hence, if it moves towards the right, a leftwards force will appear indicating a counter-clockwise induced current. ​

FluxDensity.png

  • Loop wire and a wire with increasing current: Magnetic flux is increasing into the page. Hence, to oppose the increase in magnetic flux (inside the loop), a magnetic field out of the page must exist, and thus, a counter-clockwise current is induced.​

wireloop.png

 
  • Bar magnet through a loop of wire:

    • When approaching the loop, magnetic flux is increasing, and thus, magnetic field must oppose the increase, with a counter-clockwise current.

    • When leaving the loop, the magnetic flux is decreasing, and the current is now clockwise. ​

7.jpeg

The opposite magnet (south pole first) would have the exact opposite effect.

ELECTROMAGNETIC INDUCTION

THE EXPERIMENTS OF FARADAY AND HENRY  

The discovery and understanding of electromagnetic induction are based on a long series of experiments carried out by Faraday and Henry. These experiments are illustrated by the following figures.
When the bar magnet is pushed towards the coil, the pointer in the galvanometer G deflects.
Current is induced in coil C

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