Question

A symmetric star shaped conducting wire loop is carrying a steady state current $I$ as shown the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is

• A. $\frac{{\mu }_{0}I}{4\pi a}6[\sqrt{3}-1]$
• B. $\frac{{\mu }_{0}I}{4\pi a}3[\sqrt{3}-1]$
• C. $\frac{{\mu }_{0}I}{4\pi a}6[\sqrt{3}+1]$
• D. $\frac{{\mu }_{0}I}{4\pi a}3[2-\sqrt{3}]$

Answer 1

The correct option is A $\frac{{\mu }_{0}I}{4\pi a}6[\sqrt{3}-1]$

$B=\frac{{\mu }_{0}I}{4\pi a}(sin{60}^0-sin{30}^0)$

$=\frac{{\mu }_{0}I}{4\pi a}[\frac{\sqrt{3}}{2}-\frac{1}{2}]+\frac{{\mu }_{0}I}{4\pi a}[\frac{\sqrt{3}}{2}-\frac{1}{2}]$

$B=\frac{{\mu }_{0}I}{4\pi a}\times 6[\sqrt{3}-1]$

Hence correct answer is A.