Question

A closed circuit is in the form of a regular
hexagon of side a. If the circuit carries a
current I, what is magnetic induction at the
centre of the hexagon?​

Answer 1

Suppose that the current I flows through the hexagonal loop ABCDEF of each side= a.

The magnetic field produced at the point O due to each of the six sides of the hexagonal loop is same and perpendicular to its plane (in outward direction).

Here is the solution:—

If perpendicular distance of the point O from the side AB (that is OM=r), then magnetic field at the point O due to the side AB of the loop= B(AB)

The magnetic field due to the whole hexagonal loop, B (loop)= 6 x B(AB)

B (loop) = √3μI/πa

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