A part of an infinitely long current carrying wire is bent into a circular shape as shown in the diagram. The magnetic field at the centre of the circle is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{μ_0I}{2πr}(π-1)$ normally inward
Magnetic field due to circular loop of radius $r$ at centre:
$B_{circle} = \frac{\mu_0 I}{2r}$
Magnetic field due to infinitely long straight wire at perpendicular distance $r$:
$B_{wire} = \frac{\mu_0 I}{2 \pi r}$
Both fields act in the opposite direction. Hence, net magnetic field is:
$B = \frac{\mu_0 I}{2r} - \frac{\mu_0 I}{2 \pi r}$
Final Answer: $B = \frac{\mu_0 I}{2r}\left(1 - \frac{1}{\pi}\right)$