A current I flowing through the sides of an equilateral triangle of side a. The magnitude of the magnetic field at the centroid of the triangle is
Answer & explanation
Correct answer: option 3
The correct answer is Option 3: $\frac{9μ_0I}{2πа}$
$B = 3[\frac{\mu_0 I (sin\alpha + sin\beta)}{4\pi r}$]
$\text{here } \alpha = \beta = 60°$
$r = \frac{a}{2\sqrt 3}$
$\Rightarrow B = 3[\frac{\mu_0 I (\sin 60+ \sin 60)}{4\pi r}] = 3[\frac{\mu_0 I \sqrt 3}{4\pi r}] = \frac{9\mu_0 I }{2\pi a}$