Question

A wire bent in the form of an equilateral triangle ABC of side a carries a current i. Find the magnetic field at a point having equal distance a from A, B and C

• A. $\frac{\mu_{0}i}{2\pi a}$
• B. $\frac{\mu_{0}i}{2\sqrt{3}\pi a}$
• C. $\frac{\mu_{0}i}{\sqrt{3}\pi a}$
• D. $\frac{2\mu_{0}i}{2\pi a}$

Answer 1

Answer: (B)

$\frac{\mu_{0}i}{2\sqrt{3}\pi a}$

Answer 2

Magnetic field due to one side

$\frac{\mu_{0}i}{2\sqrt{3}\pi a}$

Resultant magnetic field

B = 3B₁ cos $\left( \frac{\pi}{2} - \varphi \right)$= 3$\left( \frac{\mu_{0}i}{2\sqrt{3}\pi a} \right)\left( \frac{\frac{a}{2\sqrt{3}}}{\frac{\sqrt{3}a}{2}} \right)$ =$\frac{\mu_{0}i}{2\sqrt{3}\pi a}$