A current carrying circular loop having n number of turns per unit len

A current carrying circular loop having n number of turns per unit length has a current I through it. If the current through it and the number of turns per unit length are doubled, then the magnetic field at the centre of the loop will:

remain same.

increase by four times.

increase by two times.

decrease by two times.

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC Geoscientist – 2020

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The magnetic field at the center of a current carrying circular loop with N turns and current I is given by the formula B = (μ₀ * N * I) / (2 * R), where R is the radius of the loop. The question states ‘n number of turns per unit length’ which is unusual phrasing for a simple loop, but if interpreted as relating to the total number of turns N, then B is directly proportional to both the number of turns N and the current I (B ∝ N * I). If the number of turns (assuming N = n) is doubled and the current I is also doubled, the new magnetic field B’ will be proportional to (2N) * (2I) = 4 * (N * I). Thus, the magnetic field will increase by four times.

The magnetic field produced by a current-carrying coil (like a loop or solenoid) is directly proportional to the number of turns in the coil and the current flowing through it.

While the phrase “turns per unit length” is typically associated with solenoids or toroids, where the magnetic field inside is B = μ₀ * n * I (with n being turns per unit length), the proportionality B ∝ n * I still holds. Doubling both n (or N) and I will result in the magnetic field increasing by a factor of 2 * 2 = 4, regardless of the specific geometry, as long as the formula is proportional to n*I.

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