Question

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

• A. $B\parallel v$
• B. it is along the line joining the electron and point of observation.
• C. it obeys inverse cube law.
• D. $B\perp v$

Answer 1

The correct option is D $B\perp v$

According to Biot-Savart's law, the magnetic field $B$ at a point distance $r$ from a charge $q$ moving with a velocity $\overrightarrow{v}$ is given by,

$\overrightarrow{B}=\frac{{\mu }_o}{4\pi }\frac{q(\overrightarrow{v}\times \overrightarrow{r})}{\overrightarrow{r^3}}$

Where,

${\mu }_o$ is magnetic permeability in vacuum,
$q$ is charge of the particle,
$v$ is constant velocity vector of particle,
$r$ is the displacement vector

As we know, the direction of $\overrightarrow{B}$ is along $(\overrightarrow{v}\times \overrightarrow{r})$, i.e., perpendicular to the plane containing $\overrightarrow{v}$ and $\overrightarrow{r}$.

$\text{Final Answer}:$ (𝑎)