An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of $i$ amperes and the radius of the circular loop is $r$ metres. What will be the magnetic induction at its centre?
                   
1. $\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left( \pi + 1 \right)$
2. $\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left(\pi - 1 \right)$
3. zero
4. Infinite

A current $i$ ampere flows in a circular arc of wire whose radius is $R,$ which subtend an angle $\raisebox{1ex}{$3\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ radian at its centre. The magnetic induction $B$ at the centre is:
1. $\frac{\mu_0i}{R}$
2. $\frac{\mu_0i}{2R}$
3. $\frac{2\mu_0i}{R}$
4. $\frac{3\mu_0i}{8R}$

A straight section PQ of a circuit lies along the X-axis from x=$\frac{-\mathrm{a}}{2}$ to x= $\frac{\mathrm{a}}{2}$ and carries a steady current i. The magnetic field due to the section PQ at a point X = + a will be:

1. Proportional to a             2. Proportional to $a^2$
3. Proportional to $\frac{1}{a}$           4. Zero

A circular coil of radius R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that r >> R, varies as 

1. $\frac{1}{r}$                                          

2. $\frac{1}{r^{3/2}}$

3. $\frac{1}{r^2}$                                          

4. $\frac{1}{r^3}$ 

The magnetic induction due to an infinitely long straight wire carrying a current $i$ at a distance $r$ from the wire is given by:
1. $B =\dfrac{\mu_0}{4 \pi} \dfrac{2 i}{r}$
2. $B =\dfrac{\mu_0}{4 \pi} \dfrac{r}{2 i}$
3. $B =\dfrac{4 \pi}{\mu_0} \dfrac{2 i}{r}$
4. $B =\dfrac{4 \pi}{\mu_0} \dfrac{r}{2 i}$

The magnetic induction at the centre O in the figure shown is:                                                   

 1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right)$                                   2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}\right)$                                                         

 3. $\frac{{\mathrm{\mu }}_0\mathrm{i} }{4}\left({\mathrm{R}}_1-{}_{}{}^{}\mathrm{R}_2\right)$                                      4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)$       

In the figure shown, the magnetic induction at the centre of the arc due to the current in portion AB will be

1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{r}}$                       3.  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{r}}$                       4. Zero