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Electromagnetic Fields Notes

Questions

6 questions per paper

Difficulty

Medium

Importance

High yield for PSU core subjects

Overview

Electromagnetic Fields form the backbone of electrical engineering, bridging the gap between static charges and time-varying electromagnetic waves. For PSU exams, mastering the fundamental laws and wave behavior is critical as it tests both conceptual depth and the ability to manipulate integral/differential equations quickly.

Fundamental Laws (Gauss, Faraday, Ampere)

These laws provide the governing relationships between electric and magnetic fields. Aspirants must focus on both the integral and differential forms of these equations as they are frequently tested in match-the-column or numerical calculation formats.

  • Gauss Law (Electric): Divergence of D equals volume charge density (del dot D = rho_v)
  • Gauss Law (Magnetic): Divergence of B is always zero (del dot B = 0)
  • Faraday Law: Curl of E equals negative rate of change of B (del cross E = -dB/dt)
  • Ampere Law: Curl of H equals current density plus displacement current (J + dD/dt)
  • Electric flux density D = epsilon * E
  • Magnetic flux density B = mu * H

Maxwell's Equations

Maxwell's equations synthesize the laws of electromagnetism into a unified theory. You must be able to recognize these equations in both free space and lossy media, as variations in parameters often appear in PSU exams.

  • Del dot D = rho_v
  • Del dot B = 0
  • Del cross E = -partial B / partial t
  • Del cross H = J + partial D / partial t
  • In free space, J = 0 and rho_v = 0
  • Maxwell's equations in phasor form replace partial time derivative with j*omega

Wave Propagation & Poynting Vector

Wave propagation describes how electromagnetic energy travels through media, while the Poynting vector defines the direction and magnitude of power flow. Understanding the intrinsic impedance and attenuation constant is vital for solving numerical problems.

  • Poynting Vector P = E cross H (W/m^2)
  • Intrinsic Impedance eta = sqrt(j*omega*mu / (sigma + j*omega*epsilon))
  • Phase constant beta = omega * sqrt(mu * epsilon)
  • Skin depth delta = 1 / alpha (where alpha is attenuation constant)
  • Velocity of wave v = 1 / sqrt(mu * epsilon)
  • Intrinsic impedance of free space = 377 ohms

Inductance & Capacitance Calculation

This subtopic involves calculating energy storage components based on geometry. Questions typically ask for the capacitance of parallel plates or the inductance of solenoids and coaxial cables.

  • Capacitance C = Q/V
  • Capacitance of parallel plate = epsilon*A / d
  • Inductance L = flux linkage / current (N*phi / I)
  • Inductance of a long solenoid = (mu * N^2 * A) / l
  • Energy stored in electric field = 0.5 * epsilon * E^2 (J/m^3)
  • Energy stored in magnetic field = 0.5 * mu * H^2 (J/m^3)

Formula Sheet

del dot D = rho_v

del dot B = 0

del cross E = -dB/dt

del cross H = J + dD/dt

P = E cross H

eta = sqrt(j*omega*mu / (sigma + j*omega*epsilon))

beta = omega*sqrt(mu*epsilon)

C = epsilon*A/d

L = N*phi/I

W_e = 0.5*epsilon*E^2

W_m = 0.5*mu*H^2

Exam Tip

Memorize the intrinsic impedance formula for lossy vs. lossless media, as this is the most common shortcut for quick calculation of wave parameters.

Common Mistakes

  • Confusing the differential and integral forms of Maxwell's equations or misapplying boundary conditions.
  • Ignoring the negative sign in Faraday's Law (Lenz's Law) during numerical problem solving.
  • Neglecting the displacement current term (dD/dt) when calculating the magnetic field in non-static scenarios.

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