Electromagnetic Fields and High Voltage Engineering
Electromagnetic Fields and High Voltage Engineering tests Maxwell's equations, field boundary conditions, capacitance and inductance, and insulation breakdown. HV questions emphasize field enhancement and test waveforms.
Core rules
- Maxwell equations: divergence of D equals charge density, divergence of B is zero, curl of E is negative partial B by partial t, and curl of H is J plus partial D by partial t.
- Boundary conditions: tangential E and normal B are continuous; normal D jumps by surface charge; tangential H jumps by surface current.
- Coaxial capacitance per unit length C = 2 pi epsilon/ln(b/a); energy W = 0.5 C V^2.
- Skin depth delta = sqrt(2/(omega mu sigma)); current crowds to the surface at high frequency.
- Paschen's law gives breakdown voltage as a function of pressure-distance product; nonuniform fields lower breakdown strength.
- Standard impulse is 1.2/50 microseconds; insulation coordination uses basic impulse level.
Worked example
A 1 m coaxial cable has inner radius 5 mm, outer radius 15 mm, and relative permittivity 2.5. C = 2 pi epsilon_0 epsilon_r L/ln(b/a) = 2 pi(8.854×10^-12)(2.5)(1)/ln(3). Since ln(3) = 1.0986, C = 1.266×10^-10 F = 126.6 pF. The reasoning is to keep all lengths in metres and use natural log for the radius ratio.
Traps
Using log10 instead of ln; mixing peak and RMS HV values; forgetting that D jumps at a charged boundary; and assuming uniform-field breakdown applies to point-plane gaps.