Electromagnetic Fields and High Voltage Engineering
What the exam tests
Electromagnetic Fields and High Voltage Engineering tests Maxwell’s equations, boundary conditions, capacitance/inductance, skin effect, breakdown mechanisms, and impulse testing. Expect field-based reasoning and HV laboratory principles.
Core rules
- Gauss’s law relates electric flux to enclosed charge; Ampere’s law relates magnetic field to current and displacement current.
- At a dielectric interface, tangential E is continuous and normal D is continuous for zero surface charge; at a conductor, E is normal to the surface.
- Capacitance depends on geometry and permittivity; inductance depends on geometry and permeability.
- Skin depth δ = √(2/(ωμσ)); at high frequency current crowds near the conductor surface.
- Paschen’s law gives breakdown voltage as a function of p·d; corona is local ionization near high-field points. Standard lightning impulse is 1.2/50 μs.
Worked example
A coaxial cable has inner radius a = 1 cm, outer radius b = 5 cm, and dielectric εr = 2.5. Capacitance per unit length C = 2π ε0 εr / ln(b/a). Using ε0 = 8.854×10−12 F/m, numerator = 2π×8.854×10−12×2.5 = 1.391×10−10 F/m. ln 5 = 1.609, so C = 8.65×10−11 F/m = 0.0865 μF/km. The maximum field occurs at the inner conductor, E = V/[a ln(b/a)].
Traps
Do not interchange E and D boundary conditions. Do not use peak voltage where rms is specified in insulation calculations. Paschen’s law fails at very small gaps and high pressure. In impulse tests, front time and tail time are defined from virtual origin, not simple exponential constants.