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

$$\theta_A = 360^\circ - 90^\circ = 270^\circ = \frac{3\pi}{2}\ \text{rad}$$

$$\theta_B = 360^\circ - 60^\circ = 300^\circ = \frac{5\pi}{3}\ \text{rad}$$

$$B_A = \frac{\mu_0 I_A}{4\pi R_A} \theta_A$$

$$B_B = \frac{\mu_0 I_B}{4\pi R_B} \theta_B$$

$$\frac{B_A}{B_B} = \left(\frac{I_A}{I_B}\right) \times \left(\frac{R_B}{R_A}\right) \times \left(\frac{\theta_A}{\theta_B}\right)$$

$$\frac{B_A}{B_B} = \left(\frac{2}{3}\right) \times \left(\frac{4}{2}\right) \times \left(\frac{270^\circ}{300^\circ}\right) = \left(\frac{2}{3}\right) \times 2 \times \left(\frac{9}{10}\right) = \frac{36}{30} = \frac{6}{5}$$