Electromagnetism and Magnetic Circuits
Scope
Electromagnetism and Magnetic Circuits tests magnetic flux, flux density, magnetomotive force, reluctance, permeability, B–H behaviour, Faraday’s and Lenz’s laws, inductance, and force on a current-carrying conductor.
Core rules
- Flux Φ is in webers; flux density B = Φ/A in teslas; field strength H = NI/l in A/m.
- B = μH, where μ = μ0μr and μ0 = 4π × 10⁻⁷ H/m.
- Reluctance S = l/(μA). The magnetic circuit analogue is mmf = NI = ΦS.
- Faraday’s law: induced emf e = −N dΦ/dt. The minus sign is Lenz’s law: the induced effect opposes the change producing it.
- Self-inductance L = NΦ/I; stored energy = ½LI².
- Force on a conductor: F = BIl sin θ, maximum when the conductor is perpendicular to B.
Worked example
An air-cored solenoid has 500 turns, carries 2 A, is 0.5 m long and has area 4 cm² = 4 × 10⁻⁴ m². H = NI/l = (500 × 2)/0.5 = 2000 A/m. B = μ0H = 4π × 10⁻⁷ × 2000 = 2.51 × 10⁻³ T. Φ = BA = 2.51 × 10⁻³ × 4 × 10⁻⁴ = 1.01 × 10⁻⁶ Wb. Adding an iron core raises B for the same H, but μr is not constant once the core approaches saturation.
Traps
- Using cm² without converting to m².
- Adding mmf and flux as if they were the same quantity.
- Dropping the minus sign in Faraday’s law and then contradicting Lenz’s law.
- Assuming μr remains constant at high flux density.