Question

The radius of the curved part of the wire is $R$, the linear parts are assumed to be very long. Find the magnetic induction of the field at the point $O$ if a current-carrying wire has the shape shown in figure above.

• A. $B=\frac{3{\mu }_0}{4}\frac{i}{R}$
• B. $B=\frac{{\mu }_0}{2}\frac{i}{R}$
• C. $B=\frac{2{\mu }_0}{3}\frac{i}{R}$
• D. $B=\frac{{\mu }_0}{4}\frac{i}{R}$

Answer 1

Answer: (D)

$B=\frac{{\mu }_0}{4}\frac{i}{R}$

Magnetic field at point O due to part (1) & (3)$=0$ (magnetic field along a straight line wire is always zero)

Now magnetic field at point O due to part (2) $\Rightarrow \frac{1}{2}\times \frac{{\mu }_{0}i}{2R}$

$\Rightarrow \frac{{\mu }_{0}i}{4R}$