Electromagnetic Induction Notes

Electromagnetic Induction Summary:

Electromagnetic induction is the process where a changing magnetic field produces an electric current, discovered by Faraday.

  1. Induced Emf and Current: A changing magnetic field induces an electromotive force (emf), driving current. A constant magnetic field yields no current.

  2. Magnetic Flux and Lenz’s Law:

Magnetic flux (\PhiB) measures the magnetic field through an area.

Faraday’s law: induced emf (εε) equals the rate of change of magnetic flux.

Lenz’s law: induced emf opposes the flux change.

  1. EMF Induced in a Moving Conductor: A conductor moving in a magnetic field induces an emf.

  2. Electric Generators:

AC Generator: Converts mechanical energy to AC electrical energy.

DC Generator: Converts mechanical energy to DC electrical energy using commutators.

  1. Mutual and Self-Inductance:

Mutual Inductance (M): Changing current in one coil induces emf in another.

Self-Inductance (L): Changing current in a coil induces emf in itself.

  1. Energy Stored in a Magnetic Field: Energy stored in an inductor.

  2. Transformers: Step up/down AC voltages via primary/secondary coil relationships.

Physical Quantities

Quantity

Symbol

Type

Magnetic field

𝐁\vec{𝐁}

Vector

Force

𝐅\vec{𝐅}

Vector

Magnetic flux

Φ𝐵Φ*𝐵

Scalar

Area

𝐴𝐴

Scalar

Electromotive force (Emf)

εε

Scalar

Time

𝑡𝑡

Scalar

Angle

θθ

Scalar

Resistance

𝑅𝑅

Scalar

Current

𝐼𝐼

Scalar

Permeability of free space

μ0μ*0

Scalar

Distance

𝑟𝑟

Scalar

Loop radius

𝑅𝑅

Scalar

Length

Scalar

Speed

𝑣𝑣

Scalar

Number of turns

𝑁𝑁

Scalar

Angular speed

ωω

Scalar

Mutual Inductance

𝑀𝑀

Scalar

Self Inductance

𝐿𝐿

Scalar

Energy

𝑈𝑈

Scalar

Magnetic energy density

𝑢𝐵𝑢*𝐵

Scalar

Quantity

Symbol

Type

Magnetic field

𝐁\vec{𝐁}

Vector

Force

𝐅\vec{𝐅}

Vector

Magnetic flux

Φ𝐵Φ*𝐵

Scalar

Area

𝐴𝐴

Scalar

Electromotive force (Emf)

εε

Scalar

Time

𝑡𝑡

Scalar

Angle

θθ

Scalar

Resistance

𝑅𝑅

Scalar

Current

𝐼𝐼

Scalar

Permeability of free space

μ0μ*0

Scalar

Distance

𝑟𝑟

Scalar

Loop radius

𝑅𝑅

Scalar

Length

Scalar

Speed

𝑣𝑣

Scalar

Number of turns

𝑁𝑁

Scalar

Angular speed

ωω

Scalar

Mutual Inductance

𝑀𝑀

Scalar

Self Inductance

𝐿𝐿

Scalar

Energy

𝑈𝑈

Scalar

Magnetic energy density

𝑢𝐵𝑢*𝐵

Scalar