Question

Three long wires with same current I placed at three corners of an equilateral triangles as shown in figure then the magnetic field at the centre of the triangle will be (side length of triangle is a)

Answer 1

The total strength of the magnetic field at the center $=3times$ the magnetic field at the center due to any one side. (since this is an equilateral triangle).

Magnetic field due to any one side is $\frac{{\mu }_{0}I}{2\pi R}$ where R is the perpendicular

The distance of the wire from the center which is $\frac{a}{2\sqrt{3}}$

Therefore, Total magnetic strength,

$B_{total}=3\times \frac{{\mu }_{0}I2\sqrt{3}}{2\pi a}=\frac{3\sqrt{3}{\mu }_{0}I}{\pi a}$