When a proton is released from rest in a room, it starts with an initial acceleration ${\mathrm{a}}_0$ towards the east. When it is projected towards the north with a speed ${\mathrm{v}}_0$, it moves with initial acceleration $3{\mathrm{a}}_0$ towards east. The electric and magnetic fields in the room are -

1.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{west}, \frac{{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{up}$

2.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{west}, \frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{down}$

3.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{east}, \frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}down$

4.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{east}, \frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}up$

A positively charged particle descends vertically. In which direction will the horizontal component of the earth's magnetic field deflect?

1. east

2. west

3. north

4. south

The figure shows a particle of charge q and mass m moving with velocity v along the x-axis enters a region of the uniform magnetic field. The minimum value of v so that the charge q is deflected by an angle $30°$ is

1.  $\frac{2\mathrm{qB}\left(\mathrm{b} - \mathrm{a}\right)}{\mathrm{m}}$

2.  $\frac{\mathrm{qB}\left(\mathrm{b} + \mathrm{a}\right)}{2\mathrm{m}}$

3.  $\frac{\mathrm{qB}\left(\mathrm{b} - \mathrm{a}\right)}{\mathrm{m}}$

4.  $\frac{\mathrm{qBb}}{2\mathrm{m}}$

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

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?

The unit of reduction factor of the tangent galvanometer is 

1. Ampere

2. Gauss

3. Radian

4. None of these