Question

The magnitude of the magnetic field at the center of an equilateral triangular loop of side $1\,m$ which is carrying a current of $10\, A$ is : [Take $\mu_0 = 4\pi \times 10^{-7} \; NA^{-2}]$

• A. $18\, \mu T$
• B. $3\, \mu T$
• C. $1 \, \mu T$
• D. $9 \, \mu T$

Answer 1

Answer: (A)

$18\, \mu T$

Answer 2

$B = 3 \left[\frac{\mu_{0}i}{4\pi r} \left(\sin60^{\circ}+ \sin60^{\circ}\right)\right]$ Here, $r= \frac{a}{2\sqrt{3}} = \frac{1}{2\sqrt{3}}$ $B= 3 \left[\frac{4\pi\times10^{7}\times 10\times 2\sqrt{3} }{4 \pi\times 1} \left[\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2}\right]\right]$ $B = 18 \times10^{-6} = 18\, \mu T$