First slide

Magnetic field due to a straight current carrying wire

Question

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

Moderate

A

$2 \sqrt{3} μT$
B

$4 / \sqrt{3} μT$
C

$\frac{\sqrt{3}}{4} μT$
D

Zero

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 $\vec{B_{A}}, \vec{B_{B}} and \vec{B_{C}}$ from a closed triangle as shown. Hence the resultant field at G is zero.

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