A proton and a deuteron with the same initial kinetic energy enter a magnetic field in a direction perpendicular to the direction of the field. The ratio of the radii of the circular trajectories described by them is

• 1 : 4

• $1 : \sqrt{2}$

• 1 : 1

• 1 : 2

Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance 8 Ω each. They are connected in parallel wth a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers A and B are 30° and 60° respectively. If A has 2 turns, then B must have

• 18 turns

• 12 turns

• 6 turns

• 2 turns

113.

A charged particle is moving in a magnetic field of  strength B perpendicular to the direction of the field. If q and m denote the charge and mass of the particle respectively, then the frequency of rotation of the particle is

• $\mathrm{f} = \frac{\mathrm{qB}}{2\mathrm{\pi m}}$

• $\mathrm{f} = \frac{\mathrm{qB}}{2{\mathrm{\pi m}}^2}$

• $\mathrm{f} = \frac{2{\mathrm{\pi }}^2\mathrm{m}}{\mathrm{qB}}$

• $\mathrm{f} = \frac{2\mathrm{\pi m}}{\mathrm{qB}}$

The magnetic field at the centre of a circular current carrying conductor of radius r is B_c. The magnetic field on its axis at a distance r from the centre is B_a. The value of B_c : B_a wil be

• $1 : \sqrt{2}$

• $1 : 2\sqrt{2}$

• $2\sqrt{2} : 1$

• $\sqrt{2} : 1$

Current I is flowing in conductor shaped as shown in the figure. The radius of the curved partis r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}} \left(\frac{3\mathrm{\pi }}{2} + 1\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}} \left(\frac{3\mathrm{\pi }}{2} - 1\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}} \left(\frac{\mathrm{\pi }}{2} + 1\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}} \left(\frac{\mathrm{\pi }}{2} - 1\right)$

Two tangent galvanometers A and B are identical except in their number of turns. They are connected in series. On passing a current through them, deflections of 60° and 30° are produced. The ratio of the number of turns in A and B is

• 1 : 3

• 3 : 1

• 1 : 2

• 2 : 1

A certain current on passing through a galvanometer produces a deflection of 100 divisions. When a shunt of one ohm is connected, the deflection reduces to 1 division. The galvanometer resistance is

• 100 Ω

• 99 Ω

• 10 Ω

• 9.9 Ω

A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

• uniform throughout the pipe but not zero

• zero only along the axis of the pipe

• zero at any point inside the pipe

• maximum at the centre and minimum at the edge

A galvanometer of resistance 240 Ω allows only 4% of the main current after connecting a shunt resistance. The value of the shunt resistance is

• 10 Ω

• 20 Ω

• 8 Ω

• 5 Ω

A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength is passed through the coil, the magnetic field at its centre is

• $\frac{{\mathrm{\mu }}_0\mathrm{nI}}{\left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{a}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{nI}}{2\left(\mathrm{b} - \mathrm{a}\right)}$

• $\frac{2 {\mathrm{\mu }}_0\mathrm{nI}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{nI}}{2\left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{b}}{\mathrm{a}}$