Which of the following equations represents the Ampere-Maxwell law?

The correct answer is Option (4) → \( \oint \vec{B}\cdot d\vec{l} = \mu_0 i_c + \mu_0\varepsilon_0\,d\phi_E/dt \)

Ampere's circuital law gives the line integral of \( \vec{B} \) round a closed loop in terms of the current through it. Maxwell added the displacement current \( \varepsilon_0\,d\phi_E/dt \), due to a changing electric flux, to the conduction current \( i_c \); the result is the Ampere-Maxwell law.

NCERT (2026-27):
Displacement Current – “… The generalised (and correct) Ampere’s circuital law has the same form as Eq. (8.1), with one difference: “the total current passing through any surface of which the closed loop is the perimeter” is the sum of the conduction current and the displacement current. The generalised law is

    \( \displaystyle \oint \mathbf{B}\cdot d\mathbf{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\Phi_E}{dt} \qquad (8.6) \)

and is known as Ampere-Maxwell law.”