Biot-savart Law MCQ - Practice Questions with Answers

Biot-Savart Law:-

• If a point charge q is kept at rest near a current-carrying wire, It is found that no force acts on charge. It means a current-carrying wire does not produce electric field.

• However, if the charge q is projected in the direction of the current with velocity v, then it is deflected towards the wire (q is assumed positive). There must be a field at P that exerts a force on the charge when it is projected, but not when it is kept at rest. This field is different from the electric field which always exerts a force on a charged particle whether it is at rest or in motion. This new field is called the magnetic field and is denoted by the symbol B. The force exerted by a magnetic field is called magnetic force.

• Now let’s study about Biot-Savart Law:-

The magnetic field at a point P, due to a current element, is given by:

$d\overrightarrow{B}=\frac{1}{4\pi {\epsilon }_0{c}^2}i\frac{d\overrightarrow{l}\times \overrightarrow{r}}{r^3}$

where c is the speed of light, i is the current, $d\overrightarrow{l}$ is the length-vector of the current element and $\overrightarrow{r}$ is the vector joining the current element 1
to the point $P$. The quantity $\overline{{\epsilon }_0{c}^2}$ is written as ${\mu }_0$ and is called the permeability of vacuum. Its value is $4\pi \times {10}^{-7}\mathrm{T}-\mathrm{m}/\mathrm{A}$.
So, the equation becomes:-

And the magnitude of the field is:-
$dB=\frac{{\mu }_0}{4\pi }\frac{idl\sin \theta }{r^2}$
where $\theta$ is the angle between $d\overrightarrow{l}$ and $\overrightarrow{r}$. The direction of the field is perpendicular to the plane containing the current element and the point $P$ according to the rules of cross-product. If we place the stretched right-hand palm along $d\overrightarrow{l}$ in such a way that the fingers curl towards $\overrightarrow{r}$, the cross product $d\overrightarrow{l}\times \overrightarrow{r}$ is along the thumb. Usually, the plane of the diagram contains both $d\overrightarrow{l}$ and $\overrightarrow{r}$. The magnetic field $d\overrightarrow{B}$ is then perpendicular to the plane of the diagram, either going into the plane or coming out of the plane. We denote the direction going into the plane by an encircled cross and the direction coming out of the plane by an encircled dot.