Electromagnetic Field Theory
Electromagnetic Field Theory tests vector calculus, electrostatics, magnetostatics, Maxwell equations, boundary conditions, plane waves and transmission lines. ESE Prelims asks compact numericals on capacitance, field intensity, impedance and skin depth.
Core rules
- Gauss law: closed integral of D dot dS=Qenclosed; in free space D=epsilon0E. Capacitance C=Q/V; parallel plate C=epsilon A/d.
- Boundary conditions: tangential E is continuous; normal D is continuous only without surface charge. Normal B is continuous; tangential H jumps by surface current.
- Maxwell: curl E=-dB/dt; curl H=J+dD/dt; displacement current allows wave propagation in a vacuum.
- Plane wave: E/H=eta=sqrt(mu/epsilon); in free space eta is about 377 ohm; velocity 1/sqrt(mu0epsilon0)=3x10^8 m/s.
- Skin depth delta=sqrt(2/(omega mu sigma)); it decreases with frequency and conductivity.
Worked example
A parallel-plate capacitor has A=0.01 m^2, d=1 mm and epsilonr=4. C=epsilon0 epsilonr A/d=8.854x10^-12 x4x0.01/0.001=3.54x10^-10 F=354 pF. The reasoning is to convert millimetres to metres and use relative permittivity as a multiplier, not an additive term.
Traps
Using epsilonr=4 as 4 F/m; mixing normal and tangential boundary conditions; forgetting displacement current in a capacitor; and applying free-space eta to a lossy medium. In transmission lines, check whether the line is matched before using reflection coefficient zero.