Two identical wires A a n d B have the same length L and carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If B 1 a n d B 2 are the value of magnetic induction at the centre of the circle and at the centre of the square respectively, then the ratio B 1 B 2 is

Question

Two identical wires A a n d B have the same length L and carry the same current I . Wire A is bent into a circle of radius R and wire B is bent to form a square of side a. If B 1 a n d B 2 are the value of magnetic induction at the centre of the circle and at the centre of the square respectively, then the ratio B 1 B 2 is, π 2 8, π 2 8 2, π 2 16, π 2 16 2

MARKS App · Accepted Answer

As, B 1 = μ 0 4 π × 2 π I R = μ 0 4 π × 2 π I × 2 π L ... (i) [ ∵ L = 2 π R f o r c i r c u l a r l o o p ] B 2 = μ 0 4 π × I a 2 [ s i n 45 o + s i n 45 o ] × 4 Where a = L 4 ∴ B 2 = μ 0 I 4 π L × 8 × 4 × I 2 + I 2 = μ 0 I 4 π L × 64 2 ..... (ii) Hence, B 1 B 2 = μ 0 4 π × 4 π 2 I L μ 0 I 4 π L × 64 2 Or B 1 B 2 = π 2 8 2

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