Physics - Magnetism Question with Solution | TestHub

We know that,

$\frac{B_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}}}{B_{\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s}}}={\left(1+\frac{x^2}{r^2}\right)}^{3/2}$

Given that,$B_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}}=5\sqrt{5} B_{\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s}}$

$\frac{B_{\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{e}}}{B_{\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s}}}=5\sqrt{5}$

$\therefore 5\sqrt{5}={\left[1+\frac{x^2}{{\left(0.1\right)}^2}\right]}^{3/2}$

On squaring both sides, we get

$25\times 5={\left[1+\frac{x^2}{{\left(0.1\right)}^2}\right]}^3$

$\sqrt[3]{125}=1+\frac{x^2}{{\left(0.1\right)}^2}$

$\Rightarrow 0.01+x^2=0.05$

$\Rightarrow x^2=0.05-0.01$

$\Rightarrow x^2=0.04$

$\Rightarrow x=0.2\mathrm{ m}$