Question

Magnetic field due to a current carrying conductor (straight) is $B$. Now the value of current is doubled & direction is reversed. Then the value of magnetic field $B^{\prime }$ at the same point will be :

Answer 1

From Biot- Savart's law, magnetic field at point $P$ is,

$\overrightarrow{B}=\frac{{\mu }_{0}I}{4\pi }\frac{(\overrightarrow{dl}\times \overrightarrow{r})}{r^3}$

$B=\frac{{\mu }_0}{4\pi }\frac{Idl\sin \theta }{r^2}$


Here, $r$ is the distance of the point from the current carrying conductor.

From the right-hand thumb rule, it is clear that the direction of the magnetic field at point $\text{P}$ is perpendicularly inward on the plane of paper.

$\Rightarrow dB\propto I$

Now, the value of flowing current is doubled & direction is also reversed.

So, direction of magnetic field is also reversed and

$B^{\prime }\propto 2I$

$\Rightarrow B^{\prime }=2B$

Hence, option $\left(c\right)$ is correct answer.