Q.

Three infinitely long straight current carrying wires, each carrying a current I, are placed at the vertices of an equilateral triangle of side 1 m. Then resultant magnetic induction at the centroid of the triangle is

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a

23 μT

b

4/3 μT

c

34 μT

d

Zero

answer is D.

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Detailed Solution

Centroid G of the triangle is equidistant from the conductors A, B and C. As a result, each of the three conductors produces magnetic field at G of magnitude B, but in different directions such that BA→,BB→ and BC→ from a closed triangle as shown. Hence the resultant field at G is zero.
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Three infinitely long straight current carrying wires, each carrying a current I, are placed at the vertices of an equilateral triangle of side 1 m. Then resultant magnetic induction at the centroid of the triangle is