Magnetic Effects & Magnetism

JEE Main level, numerical answer, medium

36 of 276

Question 36 of 276

The current of 5A5A flows in a square loop of sides 1m1m is placed in air. The magnetic field at the centre of the loop is X2×10−7TX\sqrt{2}\times {10}^{-7}T. The value of XX is _________.

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Answer: 40

Magnetic field at the centre of the square loop is given by,
B=4[μ0I4πd(sin⁡45∘+sin⁡45∘)]B=4\left[\dfrac{{\mu }_{0}I}{4\pi d}\left(\sin 45^{\circ}+\sin 45^{\circ}\right)\right], where dd is perpendicular distance of the centre to one of its sides.
⇒B=4×μ0×54π×12(12+12)\Rightarrow B=4\times \dfrac{{\mu }_{0}\times 5}{4\pi \times \dfrac{1}{2}}\left(\dfrac{1}{\sqrt{2}}+\dfrac{1}{\sqrt{2}}\right)
=4×10−7×5×2×2=4\times {10}^{-7}\times 5\times 2\times \sqrt{2}
=402×10−7T=40\sqrt{2}\times {10}^{-7}T

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