Question 46: Magnetism and Matter

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 :

Accepted Answer

Let's analyze each statement in detail to determine the correct answer:
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." This statement is true. According to physics, particularly when dealing with electromagnetism and Maxwell's equations, the momentum of the electromagnetic field plays a critical role in conserving momentum in systems where electromagnetic forces are at play. In situations where electric and magnetic fields vary with time, they can carry momentum. Thus, for the conservation laws to hold, including Newton's third law which states that for every action, there is an equal and opposite reaction, the momentum carried by the electromagnetic fields must be included. This is essential in scenarios such as radiation pressure where light (which can be considered an electromagnetic wave) exerts pressure on surfaces, thereby imparting momentum.
Statement (II) :
"Ampere's circuital law does not depend on Biot-Savart's law." This statement is false. Historically and mathematically, AmpÃÂ¨re's Circuital Law and Biot-Savart Law are closely related in the context of classical electromagnetism. AmpÃÂ¨re's Law, particularly in its integral form, relates the integrated magnetic field around a closed loop to the electric current passing through the loop. Biot-Savart Law, on the other hand, is used to calculate the magnetic field generated by a current-carrying element at a point in space. Although AmpÃÂ¨re's Law can be derived without directly invoking the Biot-Savart Law, the fundamental understanding and derivations of magnetic fields due to currents, as presented in many textbooks and formulations, show that both laws are manifestations of how moving charges produce magnetic fields. Moreover, the formulation of AmpÃÂ¨re's Law was later extended by Maxwell (Maxwell's addition) to include the concept of displacement current, linking it more fundamentally to the changing electric fields and closing a conceptual loop that ties it to the broader electromagnetic theory that includes the effects described by the Biot-Savart Law.
Given the above explanations:
Option D (Statement I is true but Statement II is false) is the correct answer.

Answer

Both Statement I and Statement II are false

Answer

Statement I is false but Statement II is true

Answer

Both Statement I and Statement II are true

Answer

Statement I is true but Statement II is false

Magnetism and Matter

Choose the correct answer: