$A$ 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
    $\frac{\mu_0 I \vec{r} \times d\vec{l}}{4 \pi r^3}$ (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 the current element and position vector $\vec{r}$)

Explore More

Similar Questions

The magnetic field at a perpendicular distance of $1 \,m$ from a long straight wire carrying a current of $1 \,A$ is:

Write the equation for the magnetic field on the axis of a circular current-carrying loop at a distance from the center equal to its radius.

$A$ steady electric current is flowing through a cylindrical wire. Which of the following statements is/are correct?
$(a)$ The electric field at the axis of the wire is zero.
$(b)$ The magnetic field at the axis of the wire is zero.
$(c)$ The electric field in the vicinity of the wire is zero.
$(d)$ The magnetic field in the vicinity of the wire is zero.

The magnetic field at the centre of a circular coil of radius $r$,through which a current $I$ flows,is:

Identical currents flow in two perpendicular wires,as shown in the figure. The wires are very close but do not touch. The magnetic field can be zero:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo