Question

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:

• A. Both Statement I and Statement II are false.
• B. Statement I is true but Statement II is false.
• C. Statement I is false but Statement II is true.
• D. Both Statement I and Statement II are true.

Answer 1

The Correct Option is B

Let's analyze the statements provided:

1. 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.
   • Newton's third law states that every action has an equal and opposite reaction. In the context of electromagnetic fields, when currents vary with time, the electromagnetic field can carry both energy and momentum.
   • This is because changing currents generate time-varying electromagnetic fields, which can exert forces back on the sources of the currents. Thus, for Newton's third law to hold in the presence of time-varying currents, we must consider the momentum carried by the electromagnetic field.
   • Hence, Statement (I) is true.
2. Statement (II): Ampere’s circuital law does not depend on Biot-Savart’s law.
   • Ampere's circuital law describes the relationship between the integrated magnetic field around a closed loop and the electric current that passes through the loop. It is given by \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}\).
   • Biot-Savart's law provides a way to calculate the magnetic field generated by a small segment of current. It is an elemental version from which the Ampere’s law can be derived by considering an infinite line of current.
   • Ampere’s circuital law is indeed related to Biot-Savart’s law, as they describe magnetic fields due to currents. Thus, though Ampere's law can be used independently for calculating magnetic fields in symmetrical situations, its conceptual foundations are related to Biot-Savart’s law.
   • Therefore, Statement (II) is false.

Based on our analysis, the correct answer is that Statement I is true but Statement II is false.

Answer 2

Explanation:

1. Statement I: Newton’s third law states that for every action, there is an equal and opposite reaction. When currents vary with time, the electromagnetic fields also carry momentum. For Newton’s third law to hold in such cases, this momentum must be included in the analysis. Hence, Statement I is true.
2. Statement II: Ampere’s circuital law is an independent law that relates the magnetic field around a closed loop to the electric current passing through the loop. It does not depend on Biot-Savart’s law, which describes the magnetic field generated by a current element. Hence, Statement II is false.

Conclusion: Statement I is true but Statement II is false.