Magnetism & Electromagnetic Induction

Magnetism has been known since ancient times -- lodestones (natural magnets) were used for navigation. But the real breakthrough came when scientists discovered that electricity and magnetism are deeply connected. Moving charges create magnetic fields, and changing magnetic fields create electric currents.

Magnetic Field

A magnetic field is a region around a magnet or current-carrying conductor where magnetic effects can be felt. It is represented by field lines that go from north to south pole outside the magnet.

Magnetic field due to a long straight wire (Biot-Savart Law intro): B = mu0 I / (2 pi r)

where mu0 = 4 pi x 10⁻⁷ T m/A is the permeability of free space.

Force on a Current-Carrying Conductor

When a conductor carrying current I is placed in a magnetic field B:

F = BIL sin theta

where L is the length of conductor and theta is the angle between I and B. This is the principle behind electric motors.

Faraday's Law of Electromagnetic Induction

Michael Faraday discovered that a changing magnetic flux through a circuit induces an EMF (voltage).

Induced EMF: epsilon = -N d(phi)/dt

where N is the number of turns and phi = BA cos theta is the magnetic flux.

In simple terms: a changing magnetic field creates electricity. This is how generators work.

Lenz's Law

The direction of the induced current is such that it opposes the change that produced it. This is consistent with conservation of energy.

Example: If a magnet is pushed into a coil, the induced current creates a magnetic field that repels the magnet.

Worked Example

A coil of 100 turns has a magnetic flux of 0.02 Wb through it. If this flux is reduced to zero in 0.01 s, find the induced EMF.

Solution:

• epsilon = N x change in flux / time
• epsilon = 100 x (0.02 - 0) / 0.01
• epsilon = 100 x 2 = 200 V

Applications

• Generators/Dynamos: Convert mechanical energy to electrical energy using electromagnetic induction. Nepal's hydroelectric plants use this principle.
• Transformers: Step up or step down voltage for power transmission
• Induction cooktops: Use changing magnetic fields to heat cooking vessels

Key Takeaways

• Moving charges produce magnetic fields; changing magnetic fields produce electric currents
• Faraday's law: induced EMF = -N d(phi)/dt
• Lenz's law ensures the induced current opposes the cause
• Generators, transformers, and motors are all based on electromagnetic principles