Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct?

                       

(1) Couple on loop P will be the highest

(2) Couple on loop Q will be the highest

(3) Couple on loop R will be the highest

(4) Couple on loop S will be the highest

A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}\mathrm{th}$ to its value at the centre of the coil, is

(1) $\frac{\mathrm{R}}{\sqrt{3}}$                       

(2)  $\mathrm{R}\sqrt{3}$

(3) $2\sqrt{3}\mathrm{R}$                     

(4) $\frac{2}{\sqrt{3}}\mathrm{R}$

Which among the following options needs to be decreased to increase the sensitivity of a moving coil galvanometer?

A metallic loop is placed in a magnetic field. If a current is passed through it, then

(1) The ring will feel a force of attraction

(2) The ring will feel a force of repulsion

(3) It will move to and fro about its centre of gravity

(4) None of these

A straight wire carrying a current i is turned into a circular loop. If the magnitude of the magnetic moment associated with it in M.K.S. unit is M, the length of wire will be

1. $4\mathrm{\pi iM}$                          2. $\sqrt{\frac{4\mathrm{\pi M}}{i}}$

3. $\sqrt{\frac{4\mathrm{\pi i}}{M}}$                        4. $\frac{M\mathrm{\pi }}{4i}$

A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field $B=0.2Wb/m^2$. The torque acting on the coil is

(a) 0.32 Nm tending to rotate the side AD out of the page

(b) 0.32 Nm tending to rotate the side AD into the page

(c) 0.0032 Nm tending to rotate the side AD out of the page

(d) 0.0032 Nm tending to rotate the side AD into the page

A current of 5 amperes is flowing in a wire of length 1.5 meters. A force of 7.5 N acts on it when it is placed in a uniform magnetic field of 2 Tesla. The angle between the magnetic field and the direction of the current is:

1. 30$°$                     2. 45°

3. 60°                     4. 90°

The field normal to the plane of a coil of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the field at the centre by the fraction

(1) $\frac{3}{2}\frac{{\mathrm{h}}^2}{{\mathrm{r}}^2}$                       

(2) $\frac{2}{3}\frac{{\mathrm{h}}^2}{{\mathrm{r}}^2}$

(3)  $\frac{3}{2}\frac{{\mathrm{r}}^2}{{\mathrm{h}}^2}$                       

(4) $\frac{2}{3}\frac{{\mathrm{r}}^2}{{\mathrm{h}}^2}$ 

A proton of mass $1.67\times {10}^{-27}kg$ and charge $1.6\times {10}^{-19}C$ is projected with a speed of $2\times {10}^{6}m/s$ at an angle of $60°$ to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of the proton is:

1. A circle of radius = 0.2 m and time period $\mathrm{\pi }\times {10}^{-7}\mathrm{s}$

2. A circle of radius = 0.1 m and time period $2\mathrm{\pi }\times {10}^{-7}\mathrm{s}$ 

3. A helix of radius = 0.1 m and time period $2\mathrm{\pi }\times {10}^{-7}\mathrm{s}$

4. A helix of radius = 0.2 m and time period $4\mathrm{\pi }\times {10}^{-7}\mathrm{s}$