An element $\Delta l=\Delta x \hat{ i }$ is placed at the origin and carries a large current $I=10\; A$ (Figure). What is the magnetic field on the $y$ -axis at a distance of $0.5 \;m . \Delta x=1\; cm$
An element $\Delta l=\Delta x \hat{ i }$ is placed at the origin and carries a large current $I=10\; A$ (Figure). What is the magnetic field on the $y$ -axis at a distance of $0.5 \;m . \Delta x=1\; cm$
$| d B |=\frac{\mu_{0}}{4 \pi} \frac{I d l \sin \theta}{r^{2}}$
$d l=\Delta x=10^{-2} \,m , I=10 \,A ,$
$r=0.5 m =y, \mu_{0} / 4 \pi=10^{-7} \frac{ Tm }{ A }$
$\theta=90^{\circ} ; \sin \theta=1$
$| d B |=\frac{10^{-7} \times 10 \times 10^{-2}}{25 \times 10^{-2}}=4 \times 10^{-8} \,T$
The direction of the field is in the $+ z$ -direction. This is so since, $d l \times r =\Delta x \hat{ i } \times y \hat{ j }=y \Delta x(\hat{ i } \times \hat{ j })=y \Delta x \hat{ k }$
$\hat i \times \hat j = \hat k;\hat j \times \hat k = \hat i;\hat k \times \hat i = \hat j.$
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