Magnetic Effects & Magnetism

JEE Main level, single correct, medium

93 of 276

Question 93 of 276

An electric current is flowing through a circular coil of radius R\mathrm{R}. The ratio of the magnetic field at the centre of the coil and that at a distance 22R2 \sqrt{2} R from the centre of the coil and on its axis is :

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Answer: (B) 27

Given :: Radius =R=R
Distance x=22R\mathrm{x}=2 \sqrt{2} \mathrm{R}
Bcentre Baxis =(1+x2R2)3/2=(1+(22R)2R2)3/2=(9)3/2=27\begin{aligned} \frac{B_{\text {centre }}}{B_{\text {axis }}} & =\left(1+\frac{x^2}{R^2}\right)^{3 / 2}=\left(1+\frac{(2 \sqrt{2} R)^2}{R^2}\right)^{3 / 2} \\ & =(9)^{3 / 2}=27 \end{aligned}

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