Question

A straight wire extends from $(0,0,-5)$ m to $(0,0+5)$ m and carries a current of $2$A in $+z$ direction. Magnetic field at $(3,4,0)$ m is

• A. $\frac{2\sqrt{2}}{5}\times {10}^{-7}T$
• B. $\frac{2}{5}\times {10}^{-7}T$
• C. $\frac{\sqrt{2}}{5}\times {10}^{-7}T$
• D. None of these

Answer 1

The correct option is A $\frac{2\sqrt{2}}{5}\times {10}^{-7}T$

Wire extends only along z - axis.
$\therefore$ magnetic field can be written as
$B=\frac{{\mu }_{0}i}{4\pi d}[\text{cos}{45}^{\circ }+\text{cos}{45}^{\circ }]$
$|\overrightarrow{B}|=\frac{{\mu }_{0}i}{4\pi d}\left(2\right)\text{cos}{45}^{\circ }$
$|\overrightarrow{B}|=\frac{(4\pi \times {10}^{-7})\left(2\right)\left(2\right)\left(\frac{1}{\sqrt{2}}\right)}{4\pi \left(5\right)}T$
$|\overrightarrow{B}|=\frac{2\sqrt{2}}{5}\times {10}^{-7}T$