Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

Solution

Physics sir · 3 steps

Look for the time derivative: only Faraday's law has a term that comes alive when fields change.

1. Static versus changing. In static conditions, charges sit still or currents are steady, so no field changes with time. Any equation with a ∂/(∂ t) term is the one written for time-varying fields.

   Option	Law	Static fields	Time-varying fields
   (a) ∮ E⃗ · dl⃗ = 0	Electrostatic field is conservative	holds	fails: a changing φ_B makes a non-zero loop integral
   (b) ∮ B⃗ · dl⃗ = μ₀ I	Ampere's law, no displacement current	holds for steady currents	fails: needs the extra μ₀ ε₀ dφ_E/dt term
   (c) ∮ E⃗ · dl⃗ = -(∂ φ_B)/(∂ t)	Faraday's law	the (∂ φ_B)/(∂ t) term is zero, so it says nothing beyond (a)	holds: it is the law for changing fields
   (d) ∮ D⃗ · dA⃗ = Q	Gauss's law	holds	holds

2. Why (c) stands out. With fields frozen in time, φ_B does not change and Faraday's law collapses to ∮ E⃗ · dl⃗ = 0. That is the static statement, which is option (a). The form in (c), with -(∂ φ_B)/(∂ t), only has meaning when B⃗ changes.
3. So. The equation written for time-varying conditions, and not the one used for statics, is Faraday's law, option (c).

The idea to keep. Sort Maxwell's equations by whether they carry a time derivative. Gauss's laws hold always; ∮ E⃗ · dl⃗ = 0 and Ampere's law without displacement current are static-only versions.

Answer from the NTA final answer key. Solution by PrepWiser.