GATE 2017 EE – Question 54
The magnitude of magnetic flux density (B) in micro Teslas ($\mu$T), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current ($I$ = 1 A), and placed in vacuum as shown in the figure is ________. (Give the answer up to two decimal places.)
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.65 to 0.75
Explanation
The distance from the centre to each side is $d = \frac{\sqrt{3}}{2}$ m. For one straight side, $B = \frac{\mu_0 I}{4\pi d}(\sin\theta_1 + \sin\theta_2)$, and each end of the side makes 30° at the centre, so $B_{side} = \frac{10^{-7} \times 1}{0.866} \times (0.5 + 0.5) = 1.1547 \times 10^{-7}$ T. The six sides add in the same direction, so $B = 6 \times 1.1547 \times 10^{-7} = 0.69\ \mu$T.