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 closed-loop (of any shape) carrying current lies in the x-y plane. What happens when a uniform magnetic field B is present in the region such that the loop experiences zero force?

A circular loop with a radius of 20 cm is placed in a uniform magnetic field B = 2T in the XY plane as shown in the figure. If the loop carries a current of i = 1 A, then the magnitude of torque acting on the loop will be:
       
1.  0.25 N-m

2.  5.2 N-m

3.  2.5 N-m

4.  0.52 N-m

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?

If an electron of velocity $\left(2\hat{\mathrm{i}}\right)$ $+$ $3\hat{j}$ is subjected to a magnetic field of \(4\hat{\mathrm{k}}\) :

The unit of reduction factor of the tangent galvanometer is 

(1) Ampere

(2) Gauss

(3) Radian

(4) None of these