Question

If an electron is moving with velocity $\overrightarrow{v}$ produces a magnetic field $\overrightarrow{B}$, then

• A. the direction of the field $\overrightarrow{B}$ will be the same as the direction of velocity $\overrightarrow{v}$
• B. the direction of the field $\overrightarrow{B}$ will be the opposite as the direction of velocity $\overrightarrow{v}$
• C. the direction of the field $\overrightarrow{B}$ will be perpendicular to the direction of velocity $\overrightarrow{v}$
• D. the direction of the field $\overrightarrow{B}$ does not depend upon the direction of velocity $\overrightarrow{v}$

Answer 1

The correct option is C

the direction of the field $\overrightarrow{B}$ will be perpendicular to the direction of velocity $\overrightarrow{v}$

Magnetic field due to a current element: Any current-carrying conductor will produce a magnetic field around it. Biot-Savart's law is applicable to such situations.

Step 1: Given

Magnetic field $\overrightarrow{B}$

Velocity $\overrightarrow{v}$

Step 2: Determine the direction

Biot-Savart's law: According to this law, the magnetic field due to a tiny current element at any point is proportional to the length of the current element, the current, the sine of the angle between the current direction and the line joining the current element and the point, and inversely proportional to the square of the distance of that point.

$\overrightarrow{B}=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{q(\overrightarrow{v}\times \overrightarrow{r})}{r^3}$

$\Rightarrow$The direction of $\overrightarrow{B}$will be along $\overrightarrow{v}\times \overrightarrow{r}$

That is, it will be perpendicular to the plane containing $\overrightarrow{v}$and $\overrightarrow{r}$.

Hence, option (C) is the correct option.