Question

As shown in the figure, a current of $2 A$ flowing in an equilateral triangle of side $4 \sqrt{3} \,cm$. The magnetic field at the centroid $O$ of the triangle is

(Neglect the effect of earth's magnetic field)

• A. $4 \sqrt{3} \times 10^{-4} T$
• B. $\sqrt{3} \times 10^{-4} T$
• C. $4 \sqrt{3} \times 10^{-5} T$
• D. $3 \sqrt{3} \times 10^{-5} T$

Answer 1

Answer: (D)

$d \tan 60^{\circ}=2 \sqrt{3} $
$ d =2 \,cm $
$ B =3 \times \frac{\mu_0 i }{2 \pi d } \sin 60^{\circ} $
$ =3 \times \frac{2 \times 10^{-7} \times 2}{2 \times 10^{-2}} \times \frac{\sqrt{3}}{2}$
$ =3 \sqrt{3} \times 10^{-5}$