A circular coil of wire of radius 'r' has 'n' turns and carries a current 'I'. The magnetic induction (B) at a point on the axis of the coil at a distance $\sqrt{3}r$ from its center is :

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

2.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{8\mathrm{r}}$

3.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{16\mathrm{r}}$

4.  $\frac{{\mathrm{\mu }}_0\mathrm{In}}{32\mathrm{r}}$

The dots in the figure depict a magnetic field that is perpendicular to the plane of the paper and emanates from it. The trajectory of a particle in the plane of the paper is depicted by the curve \(ABC\). What exactly is the particle?

An electron is traveling along the x-direction. It encounters a magnetic field in the y-direction. Its subsequent motion will be:

1.  Straight-line along the x-direction

2.  A circle in the xz-plane

3.  A circle in the yz-plane

4.  A circle in the xy-plane

When an electron enters perpendicularly in a magnetic field with velocity v, time period of its revolution is T. If it enters in the same magnetic field with a velocity 2v, then its time period will be:

1.  2T

2.  4T

3.  $\frac{\mathrm{T}}{2}$

4.   T

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

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