Assertion: Amperes circuital law relates the magnetic field around a closed loop to the current flowing through the loop.Reason: Amperes circuital law is a consequence of Faradays law of electromagnetic induction.a)Both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion.b)Both the Assertion and Reason are true, but the Reason is not the correct explanation of the Assertion.c)The Assertion is true, but the Reason is false.d)The Assertion is false, but the Reason is true.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Assertion: Ampere's circuital law relates the magnetic field around a closed loop to the current flowing through the loop.

Reason: Ampere's circuital law is a consequence of Faraday's law of electromagnetic induction.

Explanation:
Ampere's circuital law states that the line integral of the magnetic field around any closed loop is equal to the permeability of free space times the total current passing through the loop. Mathematically, it can be expressed as:

∮ B · dl = μ₀I

where B is the magnetic field, dl is an infinitesimal length element along the closed loop, μ₀ is the permeability of free space, and I is the total current passing through the loop.

This law is a fundamental principle in electromagnetism and is used to calculate the magnetic field produced by a current-carrying conductor. It is based on the observation that a current-carrying wire produces a magnetic field around it.

On the other hand, Faraday's law of electromagnetic induction states that a changing magnetic field induces an electromotive force (EMF) in a closed loop. It quantifies the relationship between the rate of change of magnetic flux through a loop and the induced EMF. Mathematically, it can be expressed as:

∮ E · dl = -dΦ/dt

where E is the induced electric field, dl is an infinitesimal length element along the closed loop, dΦ/dt is the rate of change of magnetic flux through the loop.

While Faraday's law describes the induction of an electric field due to a changing magnetic field, it does not directly relate to the magnetic field produced by a current-carrying conductor. Ampere's circuital law, on the other hand, directly relates the magnetic field to the current flowing through a closed loop.

Therefore, the Assertion is true as Ampere's circuital law does relate the magnetic field around a closed loop to the current flowing through the loop. However, the Reason is false as Ampere's circuital law is not a consequence of Faraday's law of electromagnetic induction.

Answer

Ampere's circuital law relates the magnetic field around a closed loop to the current enclosed by the loop, not necessarily the current flowing through the loop itself. It states that the line integral of the magnetic field along a closed loop is equal to the product of the permeability of free space and the total current enclosed by the loop.

Ampere's circuital law is one of the fundamental laws of electromagnetism and is used to calculate the magnetic field produced by a current-carrying conductor or a set of current-carrying conductors.

While Ampere's circuital law is indeed related to the magnetic field and current, it is not a direct consequence of Faraday's law of electromagnetic induction. Faraday's law deals with the relationship between a changing magnetic field and the induced electromotive force (emf) in a conducting loop.

Therefore, the Assertion is true, but the Reason is false.

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