Question

A coil of radius $\pi$ meters, $100$ turns carries a current of $3A$. The magnetic induction at a point on its axis at a distance equal to $\sqrt{3}$ times its radius from its centre is :

• A. $7.2\times {10}^{-6}Wb{m}^{-2}$
• B. $7.4\times {10}^{-6}Wb{m}^{-2}$
• C. $7.5\times {10}^{-6}Wb{m}^{-2}$
• D. $7.83\times {10}^{-6}Wb{m}^{-2}$

Answer 1

Answer: (C)

$7.5\times {10}^{-6}Wb{m}^{-2}$

$B=\frac{{\mu }_{0}i{a}^2}{2(a^2+x^2{)}^{\frac{3}{2}}}$

$B=\frac{{\mu }_0\times 3\times {\pi }^2}{2(a^2+3a^2{)}^{\frac{3}{2}}}$

$B=\frac{4\pi \times {10}^{-7}\times 3\times {\pi }^2}{2\times 8\times {\pi }^3}$

$B=7\cdot 5\times {10}^{-6}T$