For the magnetic field to be maximum due to a small element of current-carrying conductor at a point, the angle between the element and the line joining the element to the given point must be:

1. 0°                           
2. 90°
3. 180°                        
4. 45°

Adjoining figure shows a rectangular loop of conductor carrying a current i. The length and breadth of the loop are respectively a and b. The magnetic field at the centre of loop is:-

1. $\frac{{\mu }_{0}i(a+b)}{2\pi \sqrt{a^2+b^2}}$

2. $\frac{{\mu }_{0}iab}{2\pi \sqrt{a^2+b^2}}$

3. $\frac{{\mu }_{0}i(a+b)}{\pi \sqrt{a^2+b^2}}$

4. $\frac{2{\mu }_{0}i\sqrt{a^2+b^2}}{\pi ab}$

Two wires of large length carry equal currents each i. One wire is kept along x-axis and the other is kept along y-axis. The magnitude of magnetic field at a point on z-axis at distance d from the origin is

1. $\frac{{\mu }_{0}i}{2\mathrm{\pi d}}$

2. $\frac{{\mu }_{0}i}{\sqrt{2}\mathrm{\pi d}}$

3. $\frac{{\mu }_{0}i}{\mathrm{\pi d}}$

4. zero

A current-carrying wire is placed in non-conducting liquid medium of refractive index n and relative electrical permittivity ${\epsilon }_r$. Then magnetic field at a point r distance of the point from the element is given by

1. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{l\overrightarrow{dl}\times \hat{r}}{r^2}$

2. $\frac{{\mu }_0{\mu }_r}{4\mathrm{\pi }}\frac{l\overrightarrow{dl}\times \hat{r}}{r^2}$

3. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{I\overrightarrow{dl}\times \hat{r}}{r^2}\left(\begin{array}{c}\frac{n^2}{{\epsilon }_r}\end{array}\right)$

4. Both (2) & (3)

To which law of electricity is Biot Savart law of magnetism analogous to

1. Coulomb's law

2. Ohm's law

3. Kirchoff's law

4. Faraday's law

Biot-Savart law indicates that the moving electrons (velocity \(v\)) produce a magnetic field \(B\) such that:

An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10~\text A\) (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5~\text m?\) 
\((\text{Given}~\Delta x=1~\text{cm})\)

The SI unit of magnetic field intensity is
1.  $Am{N}^{-1}$
2.  $N{A}^{-1}{m}^{-1}$
3.  $N{A}^{-2}{m}^{-2}$
4.  $N{A}^{-1}{m}^{-2}$