Đáp án:
\(\begin{array}{l}
x = 8,5\\
{B_{\max }} = 3,{32.10^{ - 5}}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
{B_1} = {B_{}} = {2.10^{ - 7}}\frac{I}{x}\\
B = 2{B_1}\cos \alpha = {2.2.10^{ - 7}}\frac{I}{x}\frac{{\sqrt {{x^2} - {{\frac{d}{2}}^2}} }}{x} = {4.10^{ - 7}}\sqrt {\frac{1}{{{x^2}}} - \frac{{{d_2}}}{{4{x^4}}}} \\
{B_{\max }} \Rightarrow \frac{1}{{{x^2}}} - \frac{{{d^2}}}{{4{x^4}}} = \frac{4}{{{d^2}}}.\frac{{{d^2}}}{{4{x^2}}}.(1 - \frac{{{d^2}}}{{4{x^2}}})\\
\frac{4}{{{d^2}}}.\frac{{{d^2}}}{{4{x^2}}}(1 - \frac{{{d^2}}}{{4{x^2}}})max \Leftrightarrow \frac{{{d^2}}}{{4{x^2}}} = 1 - \frac{{{d^2}}}{{4{x^2}}}\\
\Rightarrow x = \frac{d}{{\sqrt 2 }} = 8,5\\
{B_{\max }} = 3,{32.10^{ - 5}}
\end{array}\)