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 r₁ and r₂ in which a current i is flowing. The magnetic induction at the centre of O will be:

1.  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\mathrm{r}}\left({\mathrm{r}}_1+{\mathrm{r}}_2\right)$                           

2.  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left[\frac{{\mathrm{r}}_1+{\mathrm{r}}_2}{{\mathrm{r}}_1{\mathrm{r}}_2}\right]$

3.  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}({\mathrm{r}}_1-{\mathrm{r}}_2)$                             

4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left[\frac{{\mathrm{r}}_2-{\mathrm{r}}_1}{{\mathrm{r}}_1{\mathrm{r}}_2}\right]$  

The direction of magnetic lines of forces close to a straight conductor carrying current will be:

(1) along the length of the conductor.

(2) radially outward.

(3) circular in a plane perpendicular to the conductor.

(4) helical.

A vertical wire kept in Z-X plane carries a current from Q to P (see figure). The magnetic field due to current-carrying wire will have the direction at the origin O along :

(1) OX

(2) OX'

(3) OY

(4) OY'

 The magnetic field at the centre of a coil of n turns, bent in the form of a square of side 2 l, carrying current i, is :

(a)  $\frac{\sqrt{2}{\mathrm{\mu }}_0\mathrm{ni}}{\mathrm{\pi l}}$                               (b)  $\frac{\sqrt{2}{\mathrm{\mu }}_0\mathrm{ni}}{2\mathrm{\pi l}}$

(c)  $\frac{\sqrt{2}{\mathrm{\mu }}_0\mathrm{ni}}{4\mathrm{\pi l}}$                                (d)  $\frac{2{\mathrm{\mu }}_0\mathrm{ni}}{\mathrm{\pi l}}$

In a current-carrying long solenoid, the field produced does not depend upon: