The magnetic field dB due to a small current element dl at a distance r and element carrying current i is (a) dB = (μ₀)/(4π) i² ((dl × r)/(r)) (b) dB = (μ₀)/(4π) i ((dl × r)/(r³)) (c) dB = (μ₀)/(4π) i ((dl × r)/(r)) (d) dB = (μ₀)/(4π) i² ((dl × r)/(r²))

Answer: (b). Biot-Savart law: dB = (μ₀)/(4π)(i dlsin θ)/(r²). In vector form dB = (μ₀)/(4π)(i dl)/(r²) = (μ₀)/(4π)(i dl)/(r³), since r = r/r. So the answer is (b).

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Q114NEET 1996 · AIPMTEasy

Biot-Savart Law & Circular Coils

The magnetic field $d\vec{B}$ due to a small current element $d\vec{l}$ at a distance $\vec{r}$ and element carrying current $i$ is

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Answer: (b)

Biot-Savart law: $dB = \frac{\mu_0}{4\pi}\frac{i\,dl\sin\theta}{r^2}$ .
In vector form $d\vec{B} = \frac{\mu_0}{4\pi}\frac{i\,d\vec{l}\times\hat{r}}{r^2} = \frac{\mu_0}{4\pi}\frac{i\,d\vec{l}\times\vec{r}}{r^3}$ , since $\hat{r} = \vec{r}/r$ .
So the answer is (b).

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