Ncert Exercises & Solutions

Biot-Savart law indicates that the moving electrons (velocity $v$ ) produce a magnetic field $B$ such that:

1.	$B\perp v$ .
2.	$B\parallel v$ .
3.	it obeys inverse cube law.
4.	it is along the line joining the electron and point of observation.

Hint:

d \vec{B} = \frac{I (d \vec{l} \times \vec{r})}{r^{3}}

$d\vec {B}=\frac{{I}({d} \vec {{l}} \times \vec{{r}})}{{r}^3}$

Explanation: Biot-Savart law is given by;

d \vec{B} = \frac{I (d \vec{l} \times \vec{r})}{r^{3}}

$d\vec {B}=\frac{{I}({d} \vec {{l}} \times \vec{{r}})}{{r}^3}$

According to Biot-Savart law, the direction of the magnetic field

\vec{B}

$\vec B$ can be determined using the right-hand rule. According to this rule, if you point your thumb in the direction of the velocity vector

\vec{v}

$\vec v$ and curl your fingers toward the position vector

\vec{r},

$\vec r,$ your palm will face the direction of the magnetic field

\vec{B} .

$\vec B.$
Therefore, this shows that

\vec{B}

$\vec B$ is perpendicular to both

\vec{v}

$\vec v$ and

\vec{r} .

$\vec r.$
Hence, option (1) is the correct answer.