Question

The magnitude of magnetic flux denstiy$\left(\overrightarrow{B}\right)$ at a point having normal distance d meters from an infinitely extended wire carrying current of I A is $\frac{{\mu }_{0}I}{2\pi d}$ (in SI units)
An infinitely extended wire is laid along x-axis and is carrying current of 4A in the +ve x direction.

Another infinitely extended wire is laid along the y-axis and is carrying 2 A current in the +ve y direction. ${\mu }_0$ is permeability of free space. Assume $\hat{i},\hat{j},\hat{k}$ to be unit vectors along x,y and z axes respectively.

Assuming right handed coordinate system, magnetic field intensity, $\overrightarrow{H}$ at coordinate (2, 1, 0 ) will be

• A. $\frac{3}{2\pi }\hat{k}weber/m^2$
• B. $\frac{4}{3\pi }\overrightarrow{i}A/m$
• C. $\frac{3}{2\pi }\overrightarrow{k}A/m$
• D. $0A/m$

Answer 1

The correct option is A $\frac{3}{2\pi }\hat{k}weber/m^2$

Ans : (a)

The given vectors are along the x-axis and y-axis respectively.
The point where $\overline{H}$ is to be found in (2,1,0) which is on the x-y plane
Magnetic field intensity of point P due to$4a_x$ is
$H_x=\frac{1}{2\pi \rho }a\varphi =\frac{4}{2\pi \left(1\right)}(a_x\times a_y)=\frac{2}{\pi }{a}_z$

Magnetic field intensity of point P due to$2a_y$ is
$H_y=\frac{1}{2\pi \rho }a\varphi =\frac{2}{2\pi \left(2\right)}(a_y\times a_x)=\frac{-1}{2\pi }{a}_z$
$H=H_x+H_y$
$H=\frac{1}{\pi }(2-\frac{1}{2})=\frac{3}{2\pi }{a}_z$