Magnetostatics Methods Dr. Christopher S. Baird, UMass Lowell I. Are there permanent magnets with known M ? Because the magnet is permanent, the fields it creates will be independent and additive to the rest of the problem. Solve for the fields due to the permanent magnets with the rest of the problem (free currents, materials, boundaries, etc.) absent. Depending on the geometry choose one method: Option A: 1. Calculate the magnet's volume and surface magnetic charge density: M =−∇⋅ M 2. Calculate the magnetic scalar potential due to the magnet: M = 1 4 ∫ M x ' ∣ x − x ' ∣ d x ' 3. Calculate the fields: H =−∇ M , B =0 H 0 M ( M inside is known, M outside is zero) Option B: 1. Calculate the magnet's volume and surface bound current density: J M =∇× M 2. Calculate the magnetic vector potential due to the magnet: A = 0 4 ∫ J M x ' ∣ x − x ' ∣ d x ' 3. Calculate the fields: B =∇× A , H = 1 0 B − M ( M inside is known,
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Magnetic Field, magnetic vector potential, free currents, Dr. Christopher S. Baird, linear uniform material