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.  $\frac{2\mathrm{qB}\left(\mathrm{b}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{a}\right)}{\mathrm{m}}<mspace\; width="1em"></mspace>$

2.  $\frac{\mathrm{qB}\left(\mathrm{b}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\mathrm{a}\right)}{2\mathrm{m}}<mspace\; width="1em"></mspace>$

3.  $\frac{\mathrm{qB}\left(\mathrm{b}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>\mathrm{a}\right)}{\mathrm{m}}<mspace\; width="1em"></mspace>$

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

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?

A long solenoid has 800 turns per meter length of the solenoid. A current of 1.6 A flows through it. The magnetic induction at the end of the solenoid on its axis is:

1.  $16\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

2.  $8\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

3.  $32\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

4.  $4\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{T}$

The unit of reduction factor of the tangent galvanometer is 

1. Ampere

2. Gauss

3. Radian

4. None of these

In order to pass 10% of the main current through a moving coil galvanometer of 99 ohms, the resistance of the required shunt is :

1. 9.9 Ω

2. 10 Ω

3. 11 Ω

4. 9 Ω

When a \(12~\Omega\) resistor is connected in parallel with a moving coil galvanometer, its deflection reduces from \(50\) divisions to \(10\) divisions. What will be the resistance of the galvanometer?
1. \(24~\Omega\)
2. \(36~\Omega\)
3. \(48~\Omega\)
4. \(60~\Omega\)

A voltmeter has a resistance of G ohms and range V volts. The value of resistance used in series to convert it into a voltmeter of range nV volts is :

1. nG

2. $(n-1)G$

3. $\frac{G}{n}$ 

4. $\frac{G}{(n-1)}$