Question 275 of 276

An element $\Delta l=\Delta x \hat{i}$ is placed at the origin and carries a large current $I=10 \mathrm{~A}$. The magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m}$ from the elements $\Delta x$ of $1 \mathrm{~cm}$ length is:

A$4 \times 10^{-8} \mathrm{~T}$B$10 \times 10^{-8} \mathrm{~T}$C$8 \times 10^{-8} \mathrm{~T}$D$12 \times 10^{-8} \mathrm{~T}$

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Answer: (A) $4 \times 10^{-8} \mathrm{~T}$

$\begin{aligned} \overrightarrow{\mathrm{dB}} & =\frac{\mu_0 \mathrm{I}}{4 \pi} \frac{(\overrightarrow{\mathrm{d} l} \times \overrightarrow{\mathrm{r}})}{\mathrm{r}^3}(\text { Tesla) } \\ & =\frac{10^{-7} \times 10 \times\left(\frac{1}{2} \times \frac{1}{100}\right)(+\hat{\mathrm{k}})}{\left(\frac{1}{2}\right)^3}=4 \times 10^{-8} \mathrm{~T}(+\hat{\mathrm{k}})\end{aligned}$