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JEE Main 2026 (21 Jan, Shift 2) · Displacement Current, Maxwell's Equations & Production

Displacement Current, Maxwell's Equations & Production question from JEE Main 2026 (21 Jan, Shift 2)

Q3JEE Main 2026 · 21 JAN · SHIFT 2Difficult

Displacement Current, Maxwell's Equations & Production

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, σ=10 mho/m\sigma = 10\text{ mho/m}. The ratio of maximum conduction current density to maximum displacement current density is ______.

[[ Take 14πϵ0=9×109 Nm2/C2]\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2 ]

Numerical answer type. Work it out, then open the answer.

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Answer: 1800

  1. Jc=σE0J_c = \sigma E_0 and Jd=ε0ωE0J_d = \varepsilon_0 \omega E_0 (maximum values), so JcJd=σωε0\dfrac{J_c}{J_d} = \dfrac{\sigma}{\omega \varepsilon_0}.
  2. ε0=14π×9×109\varepsilon_0 = \dfrac{1}{4\pi \times 9 \times 10^{9}}, ω=2π×108\omega = 2\pi \times 10^{8}, so ωε0=10818×109=1180\omega\varepsilon_0 = \dfrac{10^{8}}{18 \times 10^{9}} = \dfrac{1}{180}.
  3. JcJd=10×180=1800\dfrac{J_c}{J_d} = 10 \times 180 = 1800.
  4. Answer: 1800.
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