Question

The magnetic field strength at a point P distant r due to an infinite straight wire as shown in the figure carrying i is :

• A. ${\mu }_0$
• B. ${\mu }_{0}i/2\sqrt{2}r$
• C. $\left({\mu }_{0}i/\sqrt{2}\pi r\right)$
• D. $\frac{{\mu }_{o}i}{4\pi r}[2+\sqrt{2}]$

Answer 1

The correct option is D $\frac{{\mu }_{o}i}{4\pi r}[2+\sqrt{2}]$

We know,

Magnetic field due to semi-infinite wire,

$B=\frac{{\mu }_{0}I}{4\pi R}(\cos {\theta }_1+\cos {\theta }_2)$

$B_1=\frac{{\mu }_{0}I}{4\pi R}(1+\cos ({45}^0\left)\right)$

$B_2=\frac{{\mu }_{0}I}{4\pi R}(1+\cos ({45}^0\left)\right)$

${\overrightarrow{B}}_{net}=\overrightarrow{B_1}+\overrightarrow{B_2}$

$\overrightarrow{B}=\frac{{\mu }_{0}I}{4\pi R}(2+\sqrt{2})$

Option $\text{D}$ is the correct answer.