Given below are two statements :
Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account
Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law.
In the light of the above statements, choose the correct answer from the options given below :

Solution

Physics sir · 3 steps

Ampere's law and Biot-Savart's law are two forms of the same physics, so Statement II cannot stand.

1. Statement I. For steady currents, the forces between two current-carrying wires are equal and opposite, so Newton's third law holds. When currents change with time, the electromagnetic field itself carries momentum. The third law balances only once you include that field momentum, so Statement I is true.

   ∮ B⃗ · dl⃗ = μ₀ I_(enclosed)

2. Statement II. Ampere's circuital law can be derived from Biot-Savart's law. Both link the magnetic field to a steady current and give the same physical results. Ampere's law is to Biot-Savart's law what Gauss's law is to Coulomb's law. So the claim that it does not depend on Biot-Savart's law is false.
3. So. Statement I is true and Statement II is false, which is option (d).

The idea to keep. Ampere's law is Biot-Savart's law written in integral form, just as Gauss's law is Coulomb's law in integral form. For changing currents, the field's own momentum is needed to balance the third law.

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