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. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2i}{r}(\mathrm{\pi }+1)$
2. $\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2i}{r}(\mathrm{\pi }-1)$
3. Zero
4. Infinite

The magnetic induction at point P, which is 4 cm from a long current-carrying wire is 10^-8 Tesla. What would be the field of induction at a distance of 12 cm from the same current?

Two straight horizontal parallel wires carry the same current in the same direction, and d is the distance between them. You are given a small magnetic needle that is freely suspended. Which of the following positions will have the needle's orientation independent of the magnitude of the current in the wires?

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

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

Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?

What is the magnetic field at point O in the figure?
                    

1.  $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                                  
2.  $\frac{{\mu }_{0}I}{4\mathrm{\pi r}}+\frac{{\mu }_{0}I}{2\mathrm{\pi r}}$
3.  $\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$                        
4.  $\frac{{\mu }_{0}I}{4r}-\frac{{\mu }_{0}I}{4\mathrm{\pi r}}$

If the current is flowing in the south direction along a power line, then what will be the direction of the magnetic field above the power line (neglecting the earth's field)?

If a wire in the form of a square with a side ‘a’ carries a current i, then the magnetic induction at the centre of the square wire will be:
(Magnetic permeability of free space = ${\mathrm{\mu }}_0$)

A proton and an α- particle enter a uniform magnetic field perpendicularly at the same speed. If a proton takes 25 μs to make 5 revolutions, then the periodic time for the α-particle will be:

1. 50 $\mathrm{\mu }$s               

2. 25 $\mathrm{\mu }$s 

3. 10 $\mathrm{\mu }$s                 

4. 5 $\mathrm{\mu }$s