SATHEE: Moving Charges and Magnetism

Moving Charges and Magnetism - Result Question 48

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

[1996] (a) $d \vec{B} = \frac{μ_{0}}{4 π} i (\frac{\vec{d ℓ} \times \vec{r}}{r})$

(b) $d \vec{B} = \frac{μ_{0}}{4 π} i^{2} (\frac{d \vec{ℓ} \times \vec{r}}{r^{2}})$

(c) $d \vec{B} = \frac{μ_{0}}{4 π} i^{2} (\frac{d \vec{ℓ} \times \vec{r}}{r})$

(d) $d \vec{B} = \frac{μ_{0}}{4 π} i (\frac{d \vec{ℓ} \times \vec{r}}{r^{3}})$

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Answer:

Correct Answer: 49. (d)

Solution:

(d) According to Biot Savart law,

$d \vec{B} = \frac{μ_{0}}{4 π} \frac{i (d \vec{ℓ} \times \vec{r})}{r^{3}}$

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Moving Charges and Magnetism - Result Question 48

49. The magnetic field (dB→) due to a small element (dℓ) at a distance (r→) and element carrying current i is

Answer:

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