Q 12-04-207JEE MainJEE Main 2019 (9 Jan, Shift 1)Medium
A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10\ \text{A}$. The magnetic field at point $O$ will be close to
Answer: (D) $1.0\times10^{-5}\ \text{T}$
The radial segments $PQ$ and $RS$ point towards $O$, so they give no field at $O$. The arcs have radii $r_1 = 3\ \text{cm}$ and $r_2 = 5\ \text{cm}$ and subtend $\theta = 45^\circ = \pi/4$; their currents circulate in opposite senses about $O$, so
$$B = \frac{\mu_0 I\theta}{4\pi}\left(\frac1{r_1} - \frac1{r_2}\right) = 10^{-7}\times10\times\frac\pi4\left(\frac{1}{0.03} - \frac1{0.05}\right)$$
$$B = 10^{-6}\times0.785\times13.3 \approx 1.0\times10^{-5}\ \text{T}$$
Solution by Sreeraj P, M.Sc Physics