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Q72 (NDA-II/2018) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Electricity and magnetism Answer Verified

A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?

Result
Your answer: —  ·  Correct: C
Explanation

The magnetic induction (B) at the centre of a circular coil is given by the formula B = (μ₀NI) / (2R), where N is the number of turns, I is the current, and R is the radius. This indicates that the magnetic field is directly proportional to the number of turns (N) and inversely proportional to the radius (R) [1]. According to the problem, the initial magnetic induction B₁ is 0.1 tesla. When the number of turns is doubled (N' = 2N), the magnetic field doubles [1]. Simultaneously, when the radius is halved (R' = R/2), the magnetic field doubles again due to the inverse relationship. Mathematically, the new field B₂ = μ₀(2N)I / (2(R/2)) = 4 × (μ₀NI / 2R) = 4B₁. Therefore, the new magnetic induction is 4 × 0.1 tesla = 0.4 tesla.

Sources

  1. [1] Science , class X (NCERT 2025 ed.) > Chapter 12: Magnetic Effects of Electric Current > 12.2.3 Magnetic Field due to a Current through a Circular Loop > p. 201
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