Moving Charges and Magnetism

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The Lorentz force is the total force experienced by a charged particle in the presence of both electric and magnetic fields. F = q(E + v × B) Where: - F = Total force on the charge - q = Charge of t…

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1. **Velocity dependence**: Force exists only when the charge is moving (|v| ≠ 0) 2. **Perpendicular direction**: Magnetic force is always perpendicular to both velocity (v) and magnetic field (B) 3…

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The SI unit of magnetic field is **Tesla (T)**. Definition: 1 Tesla is the magnetic field strength when a charge of 1 coulomb moving with velocity 1 m/s perpendicular to the field experiences a force…

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For a straight conductor of length l carrying current I: Starting from microscopic level: - Number of charge carriers = nlA (n = number density, A = cross-section) - Each carrier has charge q and dri…

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**Case 1: v ⊥ B (velocity perpendicular to field)** - Particle follows a circular path - Magnetic force provides centripetal force - Radius: r = mv/(qB) - Frequency: ν = qB/(2πm) (cyclotron frequency)…

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**Biot-Savart Law**: The magnetic field dB due to a current element Idl at distance r is: **dB = (μ₀/4π) × (Idl × r)/r³** Where: - μ₀ = 4π × 10⁻⁷ Tm/A (permeability of free space) - dl = current ele…

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For a circular loop at the center (x = 0): Using Biot-Savart law: - Each element dl is perpendicular to r - All elements are at same distance R from center - All dB vectors point in same direction (p…

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**Ampere's Circuital Law**: ∮ B⃗ · dl⃗ = μ₀Iₑₙcₗₒₛₑd The line integral of magnetic field around any closed path equals μ₀ times the net current enclosed by that path. **Easy Application Conditions**…