Question

A current of $3.14$ $A$ flows in an infinitely long wire with cross section in the form of a semicircular ring of radius $5$ $cm$. The magnitude of magnetic induction on its axis is :

• A. $8.0$ x ${10}^{-6}$ $T$
• B. $1.6$ x ${10}^{-5}$ $T$
• C. $2.0$ x ${10}^{-5}$ $T$
• D. $4.0$ x ${10}^{-6}$ $T$

Answer 1

The correct option is A $8.0$ x ${10}^{-6}$ $T$

Magnetic Induction is given by

$B=\frac{u_{o}i}{{\pi }^{2}R}$ .......$\left(1\right)$

here $I=3.14$A

$R=5$cm$=0.05$m

$\pi =3.14$

$u_o=1.257\times {10}^{-6}$

$\therefore$ Equation $1$ becomes

$B=\frac{1.257\times {10}^{-6}\times 3.14}{(3.14{)}^2\times 0.05}$

$=\frac{1.257\times {10}^{-6}\times 3.14}{3.14\times 3.14\times 0.05}$

$=\frac{1.257\times {10}^{-6}}{0.157}$

$B=8.006\times {10}^{-6}$T.