Magnetic fields are produced by moving charges and currents. They exert forces on other moving charges and current-carrying wires. The strength and direction depend on the configuration and parameters of the system.

Key Formulas:

• Straight Wire: B = μ₀I / (2πr)
• Loop: B = μ₀I / (2r)
• Solenoid: B = μ₀nI (n = N/L)
• Bar Magnet (on axis): B = (μ₀/4π) × (2M / r³)
• Force on Wire: F = BILsinθ
• Force on Charge: F = qvBsinθ

Units:

• Magnetic Field: Tesla (T)
• Current: Ampere (A)
• Length: Meter (m)
• Charge: Coulomb (C)
• Velocity: m/s
• Angle: degrees (°)

Applications:

• Electromagnets and solenoids
• Electric motors and generators
• Magnetic resonance imaging (MRI)
• Particle accelerators
• Magnetic sensors and compasses