In Ampere-circuital law, the missing term is:

The correct answer is Option (2) → \( i = \varepsilon_0\displaystyle\frac{d\phi_E}{dt} \)

Ampere's circuital law in its original form, \( \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c \), fails between the plates of a charging capacitor, where no conduction current flows. Maxwell added the displacement current, produced by a changing electric flux:

    \( \displaystyle i_d = \varepsilon_0\,\frac{d\phi_E}{dt} \)

    \( \displaystyle \oint \vec{B}\cdot d\vec{l} = \mu_0\left(i_c + \varepsilon_0\,\frac{d\phi_E}{dt}\right) \)

So the missing term is \( i = \varepsilon_0\, d\phi_E/dt \).

NCERT (2026-27):
Displacement Current – “… The generalisation made by Maxwell then is the following. The source of a magnetic field is not just the conduction electric current due to flowing charges, but also the time rate of change of electric field. More precisely, the total current i is the sum of the conduction current denoted by i_c, and the displacement current denoted by i_d (= ε₀ (dΦ_E/dt)). So we have

    \( \displaystyle i = i_c + i_d = i_c + \varepsilon_0\,\frac{d\Phi_E}{dt} \qquad (8.5) \)”