Question

Find the magnetic field intensity due to a thin wire carrying current $I$ in the figure :

• A. $\frac{{\mu }_{0}i}{2\pi R}(\pi -a+tana)$
• B. $\frac{{\mu }_{0}i}{2\pi R}(\pi -a)$
• C. $\frac{{\mu }_{0}i}{2\pi R}(\pi +a)$
• D. $\frac{{\mu }_0}{2\pi R}(\pi +a-tana)$

Answer 1

Answer: (A)

$\frac{{\mu }_{0}i}{2\pi R}(\pi -a+tana)$

Magnetic field intensity due to arc part of wire $B_{arc}=\frac{{\mu }_{0}I}{4\pi R}(2\pi -2a)$,
Magnetic field intensity due to linear part of wire $B_{line}=\frac{{\mu }_{0}I(sin\alpha +sin\alpha )}{4\pi Rcos\alpha }$
$B_{net}=B_{arc}+B_{line}$
$B_{net}=\frac{{\mu }_{0}I}{4\pi R}(2\pi -2a),+\frac{{\mu }_{0}I(sin\alpha +sin\alpha )}{4\pi Rcos\alpha }$
$B_{net}=\frac{{\mu }_{0}I}{2\pi R}(\pi -a+tana)$