An element $d l=d x \hat{l}$ (where, $d x=1\, cm$ ) is placed at the origin and carries a large current $i=10 A$. What is the magnetic field on the $Y$ -axis at a distance of $0.5\, m$ ?
AIIMS 2018, Diffcult
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Here, $d l=d x=1 cm =10^{-2} m$,
$i=10 A , r=0.5 m$
$\therefore d B=\frac{\mu_{0}}{4 \pi} \cdot \frac{i(d l \times r)}{r^{3}}$
$=\frac{\mu_{0}}{4 \pi} \cdot \frac{i d l}{r^{2}}(\hat{\imath} \times \hat{j})=\frac{\mu_{0}}{4 \pi} \cdot \frac{i d l}{r^{2}} \hat{k}$
$=\frac{10^{-7} \times 10 \times 10^{-2} \sin 90^{\circ}}{(0.5)^{2}} \hat{k}$
$=4 \times 10^{-8} \hat{k} T$
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