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:
Statement (I): Newton’s third law requires accounting for electromagnetic field momentum when currents vary over time.
Newton's third law posits that for every action, there is an equal and opposite reaction. In electromagnetism, time-varying currents induce electromagnetic fields that can carry both energy and momentum.
These changing currents create time-dependent electromagnetic fields, which exert reactive forces on the current sources. Consequently, the momentum of the electromagnetic field must be considered for Newton's third law to remain valid with time-varying currents.
Therefore, Statement (I) is affirmed as true.
Statement (II): Ampere’s circuital law is independent of Biot-Savart’s law.
Ampere's circuital law relates the magnetic field integrated around a closed loop to the enclosed electric current, expressed as \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}\).
Biot-Savart's law allows for the calculation of the magnetic field produced by a infinitesimal current element and serves as a basis from which Ampere's law can be derived, particularly for infinite current distributions.
Ampere's circuital law and Biot-Savart's law are interconnected as both describe magnetic fields generated by currents. While Ampere's law can be applied independently in situations with symmetry, its theoretical underpinnings are linked to Biot-Savart's law.
Consequently, Statement (II) is determined to be false.
Based on this evaluation, the conclusion is that Statement I is true, while Statement II is false.
