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

A galvanometer of \(50~\Omega \) resistance has 25 divisions. A current of 4 × 10^–4 A gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of 25 V, it should be connected with a resistance of:

1. 2500 Ω as a shunt

2. 2450 Ω as a shunt

3. 2550 Ω in series

4. 2450 Ω in series

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

The electric charge in uniform motion produces :

(1) An electric field only

(2) A magnetic field only

(3) Both electric and magnetic field

(4) Neither electric nor magnetic field