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Answer this:  Assertion (A): When radius of a circular loop carrying a steady current is doubled, its magnetic moment becomes four times.  Reason (R): The magnetic moment of a circular loop carrying a steady current is proportional to the area of the loop.  Select the correct answer from the codes (a), (b), (c) and (d) as given belote.  (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).  (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).  (c) Assertion (A) is true, but Reason (R) is false.  (d) Assertion (A) is false and Reason (R) is also false. Expert Answer
The magnetic moment (m) of a current-carrying circular loop, as we know, is given by the formula:
m = IA
where I is the current flowing through the loop and A is the area of loop.
As a result we can conclude that, the given assertion (A) is correct since the magnetic moment is proportional to the area of the loop.

When the radius of the circular loop is doubled, the area of the loop becomes four times the original area (A' = 4A). Using the above formula, the magnetic moment becomes four times its original value:
i.e., m' = I(A') = I(4A) = 4IA = 4m
Hence for the given case, both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
Answered by Jayesh Sah | 06 Mar, 2023, 06:08: PM

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