Question

Solve: $\frac{4\pi \times {10}^{-7}\times 20\times 0.5\times {\left(0.1\right)}^2}{2{\left[{\left(0.1\right)}^2+{\left(0.1\right)}^2\right]}^{3/2}}$

Answer 1

$\begin{array}{c}y=\frac{4\pi \times {10}^{-7}\times 20\times 0.5\times {\left(0.1\right)}^2}{2{\left[{\left(0.1\right)}^2+{\left(0.1\right)}^2\right]}^{3/2}}\\ =\frac{4\times \pi \times 2\times {10}^{-6}\times 5\times {10}^{-1}\times 1\times {10}^{-2}}{2{\left[0.01+0.01\right]}^{3/2}}\\ =\frac{20\times \pi \times {10}^{-9}}{2{\left[0.02\right]}^{3/2}}\\ =\frac{2\times \pi \times {10}^{-8}}{{\left[2\times {10}^{-2}\right]}^{3/2}}\\ =\frac{2\times \pi \times {10}^{-8}}{2^{3/2}\times {10}^{-3}}\\ =\frac{2\times \pi \times {10}^{-8}}{{\left(\sqrt{2}\right)}^3\times {10}^{-3}}\\ =\frac{2\times \pi \times {10}^{-5}}{{\left(\sqrt{2}\right)}^3}\\ =\frac{2\times \pi \times {10}^{-5}}{2\sqrt{2}}\\ =\frac{\pi }{\sqrt{2}}\times {10}^{-5}\end{array}$