Conduction Current versus Displacement Current
For an ohmic medium, conduction-current density is sigma E. For a sinusoidal electric field of angular frequency omega, displacement-current density has amplitude omega epsilon E_0, so their amplitude ratio is sigma/(omega epsilon).
Why this shows up in the exam
Comparing dielectric and conducting behavior at high frequency · Analyzing lossy media such as seawater · Finding when conduction and displacement currents are equal
Learn the idea
Conduction current moves charge, while displacement current comes from a changing electric field. In a conductor, mobile charges drift and make conduction current. In a dielectric or vacuum gap, a changing electric field can still create the magnetic effect represented by displacement current; at high frequency it can rival conduction current.
🧠 Memory hook: Conduction follows E; displacement follows how fast E changes.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- J_c = sigma E — ohmic conduction-current density
- J_d = epsilon dE/dt — displacement-current density
- J_c0/J_d0 = sigma/(omega epsilon) — amplitude ratio for a sinusoidal field
How to approach it
- 1Write J_c and J_d separately
- 2For a sinusoid, compare amplitudes using omega epsilon
- 3Solve the ratio or equality condition with SI units
Common slip-ups that cost marks
- •Using frequency f where angular frequency omega is required
- •Comparing instantaneous currents at phases where one is zero
- •Omitting the medium permittivity from displacement current
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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