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)  $\frac{2{\mathrm{\mu }}_0\mathrm{ni}}{\mathrm{\pi l}}$

A circular coil A  has a radius \(R\) and the current flowing through it is \(I.\) Another circular coil B has a radius \(2R\) and if \(2I\) is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e. $B_A$ to $B_B$):
1. \(4:1\)                             
2. \(2:1\)
3. \(3:1\)                             
4. \(1:1\)

A straight wire of diameter 0.5 mm carrying a current of 1 A is replaced by another wire of 1 mm diameter carrying the same current. The strength of the magnetic field far away is :

(1) Twice the earlier value

(2) Half of the earlier value

(3) Quarter of its earlier value

(4) Unchanged

A wire carrying current i is shaped as shown. Section AB is a quarter circle of radius r. The magnetic field is directed :

                                                      
(a) At an angle $\mathrm{\pi }/4$ to the plane of the paper

(b) Perpendicular to the plane of the paper and directed in to the paper

(c) Along the bisector of the angle ACB towards AB

(d) Along the bisector of the angle ACB away from AB