Question

$\overrightarrow{B}$ at centroid of regular hexagon carrying current $i$ as shown is:

• A. $\frac{12}{\sqrt{3}}$ Gauss
• B. $\frac{6}{\sqrt{3}}$ Gauss
• C. $\sqrt{3}$ Gauss
• D. $\frac{1}{\sqrt{3}}$ Gauss

Answer 1

The correct option is A $\frac{12}{\sqrt{3}}$ Gauss

$B_{net}=6\times B_{oneside}$

$B_{oneside}=\frac{{\mu }_{o}i}{4\pi r}(sin\alpha +sin\beta )$

Here, $\alpha =\beta ={30}^o$

$B_{net}=\frac{6\times {10}^{-7}\times 10}{a\sqrt{3}}=\frac{12}{\sqrt{3}}\times \frac{{15}^6}{{10}^{-2}}=\frac{12}{\sqrt{3}}\times {10}^{-7}=\frac{12}{\sqrt{3}}$Gauss