Magnetism

Introduction

Magnetism is a class of physical phenomena mediated by magnetic fields. It arises from moving electric charges and is one of the fundamental forces of nature. It is closely related to electricity through the theory of electromagnetism.

Key Concepts

Magnetic Field (B)

A vector field that represents the magnetic influence on moving charges and magnetic materials.

Magnetic Force

Force on a moving charge in a magnetic field given by F = q(v × B).

Magnetic Dipole

A magnetic dipole consists of two equal and opposite magnetic poles separated by a distance.

Earth’s Magnetism

The Earth behaves like a giant magnet with magnetic poles near the geographic poles.

Important Formulas

B = μ₀I / (2πr)

Magnetic field due to a long straight current-carrying wire.

F = qvB sinθ

Magnetic force on a moving charge in a magnetic field.

Torque = MB sinθ

Torque on a magnetic dipole in a uniform magnetic field.

Magnetic Flux (Φ) = B ⋅ A

Total magnetic field passing through an area A.

Applications

Example Problems

1. Calculate the magnetic field at a distance of 5 cm from a wire carrying 10 A current.

Solution: B = (μ₀I)/(2πr) = (4π×10⁻⁷ × 10)/(2π × 0.05) = 4×10⁻⁵ T

2. Find the force on a 1 C charge moving at 2×10⁶ m/s perpendicular to a 0.2 T field.

Solution: F = qvB = 1 × 2×10⁶ × 0.2 = 4×10⁵ N

3. What is the torque on a magnetic dipole of moment 0.1 Am² in a 0.5 T field at 30°?

Solution: Torque = MB sinθ = 0.1 × 0.5 × sin(30°) = 0.025 Nm