Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If BA and BB are the values of magnetic field at the centres of the circle and. square respectively, then the ratio is :

Engineering

Physics

Biot Savart Law

Question

Two identical wires A and B, each of length 'l', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If B_A and B_B are the values of magnetic field at the centres of the circle and. square respectively, then the ratio $\frac{B_{A}}{B_{B}}$ is :

$\frac{π^{2}}{16}$

$\frac{π^{2}}{8 \sqrt{2}}$

$\frac{π^{2}}{16 \sqrt{2}}$

$\frac{π^{2}}{8}$

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$B_{A} = \frac{µ_{0} I}{2 R} = \frac{µ_{0} I (2 π)}{2 ℓ}$ [l = 2pR]

$B_{B} = 4 [\frac{µ_{0} I \sqrt{2}}{4 π \frac{a}{2}}] = \frac{2 \sqrt{2} µ_{0} I}{πa} = \frac{8 \sqrt{2} µ_{0} I}{πl}$ [l = 4a]

$\frac{Β_{A}}{B_{B}} = \frac{π^{2}}{8 \sqrt{2}}$