# A wire A, bent in the shape of an arc of a circle, carrying a current of 2A and having a radius of 2cm and another wire B, also bent in the shape of an arc of a circle, carrying a current 3A and having a radius of 4cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common center O is: Option: 1 4:6 Option: 2 6:4 Option: 3 2:5 Option: 4 6:5

$\begin{array}{l} \text { Given } \\ i_{\mathrm{A}}=2, \mathrm{r}_{\mathrm{A}}=2 \mathrm{~cm}, \theta_{\mathrm{A}}=2 \pi-\frac{\pi}{2}=\frac{3 \pi}{2} \\ \\ \mathrm{i}_{\mathrm{B}}=3, \mathrm{r}_{\mathrm{B}}=4 \mathrm{~cm}, \theta_{\mathrm{B}}=2 \pi-\frac{\pi}{3}=\frac{5 \pi}{3} \\ \\ \mathrm{~B}=\frac{\mu_{0} \mathrm{I} \theta}{4 \pi \mathrm{R}} \\ \\ \frac{\mathrm{B}_{\mathrm{A}}}{\mathrm{B}_{\mathrm{B}}}=\frac{\mathrm{I}_{\mathrm{A}}}{\mathrm{I}_{\mathrm{B}}} \times \frac{\theta_{\mathrm{A}} \mathrm{R}_{\mathrm{B}}}{\theta_{\mathrm{B}} \mathrm{R}_{\mathrm{A}}}=\frac{6}{5} \end{array}$

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