Question

A small linear segment of an electric circuit is lying on $x-$axis extending from $x=-\frac{a}{2}$ to $x=\frac{a}{2}$ and a current $i$ is flowing in it. The magnetic field due to the segment at a point $x=a$ will be

• A. $\propto a$
• B. zero
• C. $\propto a^2$
• D. $\alpha \frac{1}{a}$

Answer 1

Answer: (B)

zero

Magnetic field at a point P due to a current carrying conductor is $\overrightarrow{B}=\frac{{\mu }_0}{4\pi }I\int \frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$
For point P $\overrightarrow{dl}\parallel \overrightarrow{r}$
$\therefore \overrightarrow{dl}\times \overrightarrow{r}=0$
$\Rightarrow \overrightarrow{B}=0$