Consider a current-carrying wire as shown in | vedclass

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Question

(A) The magnetic field at point $O$ is the vector sum of the magnetic fields produced by the three segments of the wire: the two long straight parts a

Vedclass · Accepted Answer

$\frac{\mu_0}{4 \pi} \frac{i}{R}(2+\pi)$

Vedclass · Answer

(A) The magnetic field at point $O$ is the vector sum of the magnetic fields produced by the three segments of the wire: the two long straight parts and the semi-circular part.$1$. For a semi-infinite straight wire, the magnetic field at a point on the line perpendicular to the wire at its end is $B_1 = \frac{\mu_0 i}{4 \pi R}$.$2$. For a semi-circular arc of radius $R$, the magnetic field at its center is $B_2 = \frac{\mu_0 i}{4 R}$.$3$. The two straight parts are both semi-infinite and contribute equally to the magnetic field at $O$ in the same direction.$4$. Total magnetic field $B = B_{	ext{straight1}} + B_{	ext{arc}} + B_{	ext{straight2}} = \frac{\mu_0 i}{4 \pi R} + \frac{\mu_0 i}{4 R} + \frac{\mu_0 i}{4 \pi R}$.$5$. Simplifying the expression: $B = \frac{2 \mu_0 i}{4 \pi R} + \frac{\mu_0 i}{4 R} = \frac{\mu_0 i}{4 \pi R} (2 + \pi)$.

Column $I$	Column $II$
$(A)$ Two parallel wires with current in the same direction,$P$ is the midpoint.	$(p)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in the same direction.
$(B)$ Two coaxial circular loops with current in the same direction,$P$ is the midpoint on the axis.	$(q)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in opposite directions.
$(C)$ Two coplanar circular loops with current in opposite directions,$P$ is the midpoint.	$(r)$ There is no magnetic field at $P$.
$(D)$ Two concentric coplanar circular loops with current in the same direction,$P$ is the common center.	$(s)$ The wires repel each other.

Consider a current-carrying wire as shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

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