$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$, making an angle $\theta$ with the current element, then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

  • A
    $\frac{\mu_0 I (d\vec{l} \times \vec{r})}{4 \pi r^3}$ (perpendicular to the current element $d\vec{l}$)
  • B
    $\frac{\mu_0 I (\vec{r} \times d\vec{l})}{4 \pi r^2}$ (perpendicular to the current element $d\vec{l}$)
  • C
    $\frac{\mu_0 I (d\vec{l} \times \vec{r})}{4 \pi r^2}$ (perpendicular to the plane containing the current element and position vector $\vec{r}$)
  • D
    $\frac{\mu_0 I (d\vec{l} \times \vec{r})}{4 \pi r^3}$ (perpendicular to the plane containing current element and position vector $\vec{r}$)

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$A$ long straight wire carrying a current of $30 \ A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \ T$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \ cm$ away from the wire is $(\mu_0 = 4 \pi \times 10^{-7} \ H/m)$.

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