Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismBiot-savart's & Ampere's Circuital lawEasy2 minPYQ_2020

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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

Options:

Answer:

Solution:

$2 π R = 4 a$

$\frac{a}{R} = \frac{2 π}{4} \Rightarrow$ $\frac{a}{R} = \frac{π}{2}$

$B_{A} = \frac{μ_{0} i}{2 R}$

$B_{B} = \frac{μ_{0} i}{π a} (2 \sqrt{2})$

$\frac{B_{A}}{B_{B}} = \frac{μ_{0} i}{2 R} \times \frac{π a}{2 \sqrt{2} μ_{0} i}$

$= \frac{π a}{4 \sqrt{2} R} = \frac{π}{4 \sqrt{2}} (\frac{π}{2}) = \frac{π^{2}}{8 \sqrt{2}}$

Subject:PhysicsTopic:MagnetismSubtopic:Biot-savart's & Ampere's Circuital law

⏱ 2mℹ️ Source: PYQ_2020

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