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. \( B =\frac{\mu_0}{4 \pi} \frac{2 i}{r} \)
2. \(B =\frac{\mu_0}{4 \pi} \frac{r}{2 i} \)
3. \(B =\frac{4 \pi}{\mu_0} \frac{2 i}{r} \)
4. \(B =\frac{4 \pi}{\mu_0} \frac{r}{2 i}\)

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

(a) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{r}}$                       (c)  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{r}}$

(b) $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{r}}$                        (d) Zero

Two concentric circular coils of ten turns each are situated in the same plane. Their radii are 20 and 40 cm and they carry respectively 0.2 and 0.3 ampere current in opposite direction. The magnetic field in $weber/m^2$ at the centre is :

(a) $\frac{35}{4}{\mu }_0$                              (b) $\frac{{\mu }_0}{80}$
(c)  $\frac{7}{80}{\mu }_0$                              (d) $\frac{5}{4}{\mu }_0$

In the figure shown below there are two semicircles of radius \(r_1\) and \(r_2\) in which a current \(i\) is flowing. The magnetic induction at the centre of \(O\) will be: