A wire A, bent in the shape of an arc of a circle, carrying a current… | JEE Main 2020 (4 Sep, Shift 1)

Q85JEE Main 2020 · 4 SEP · SHIFT 1Medium

Biot-Savart Law & Circular Coils

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 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:

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Answer: (d)

Field of an arc: $B = \dfrac{\mu_0 I\theta}{4\pi r}$ , so $B \propto \dfrac{I\theta}{r}$ .
Arc A: gap $90^\circ$ , so $\theta_A = 270^\circ$ ; arc B: gap $60^\circ$ , so $\theta_B = 300^\circ$ .
$\dfrac{B_A}{B_B} = \dfrac{2 \times 270/2}{3 \times 300/4} = \dfrac{270}{225} = \dfrac{6}{5}$
So the answer is (d) $6 : 5$ .

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