First slide
Magnetic field due to a straight current carrying wire
Question

A current i is flowing in a hexagonal coil of side / [Fig.]. The magnetic induction at the centre of the coil will be

Moderate
Solution

See fig. Every angle of equilateral triangle is 60°

Distance OG=3l/2 The magnetic induction at O is given by
B=6×BAB
 B=6×μ0i4π(3l/2)sin30+sin30=6μ0i4π(3l/2)×2sin30=3μ0iπl

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