Magnetic Field Intensity due to Straight Filamentary Conductor

Q. The conducting triangular loop shown in figure carries a current of 10 A . The magnetic field $\overrightarrow{H}$ at point (0, 0, 5) due to side 1 of the loop is,

1. $+65.17{\hat{a}}_y$ (mA/m)
2. $-59.11{\hat{a}}_y$ (mA/m)
3. $-65.17{\hat{a}}_y$ (mA/m)
4. $+79.13{\hat{a}}_y$ (mA/m)

Q. Two parallel wires separated by a distance 'd' are carrying a current 'I' in the same direction. The magnetic field along a line running parallel to these wire and midway between them

1. Depends upon 'I'
2. Is zero
3. Depends upon 'd'
4. Depends upon the permeability of medium between the wires

Q. 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

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

Q. A steady current I is flowing in the x- direction through each of two infinitely long wires at $y=\pm \frac{L}{2}$ as shown in the figure. The permeability of the medium is ${\mu }_0$. The $\overrightarrow{B}$ field at (0, L, 0 ) is

1. $-\frac{4{\mu }_{0}I}{3\pi L}\hat{z}$
2. $+\frac{4{\mu }_{0}I}{3\pi L}$
3. 0
4. $-\frac{3{\mu }_{0}I}{4\pi L}\hat{z}$

Q. Two conductors are carrying forward and return current of $+I$ and $-I$ as shown in figure. The magnetic field intensity $\overrightarrow{H}$ at point $P$ is

1. $\frac{I}{\pi d}\overline{y}$
2. $\frac{I}{\pi d}\overline{x}$
3. $\frac{I}{2\pi d}\overline{Y}$
4. $\frac{I}{2\pi d}\overline{X}$

Q. A line carrying current of finite length is along z-direction. The direction of magnetic field intensity is

1. along ${\hat{a}}_2$ direction
2. along ${\hat{a}}_r$ direction
3. along ${\hat{a}}_p$direction
4. along ${\hat{a}}_{\varphi }$ direction

Q. Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of $H_{\varphi }$ on r, where $H_{\varphi }$ is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor?

1. 
2. 
3. 
4. 

Q. Two identical copper wires $W_{1}and{W}_2$ placed in parallel as shown in the figure, carry currents I and 2I, respectively. In opposite directions. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field $\overrightarrow{B}$ between the wires at a distance r from $W_1$ is

1. $\frac{{\mu }_0^2{I}^2}{2\pi r^2}$

2. $\frac{6{\mu }_{0}I}{5\pi r}$

3. $\frac{{\mu }_{0}I}{6\pi r}$

4. $\frac{5{\mu }_{0}I}{6\pi r}$