One proton beam enters a magnetic field of ${10}^{-4}T$ normally, Specific charge = ${10}^{11}C/kg.$ velocity = ${10}^{7}m/s.$ What is the radius of the circle described by it:

1. $0.1m$                               

2. $1m$

3. $10m$                               

4. None of these

A circular coil 'A'  has a radius R and the current flowing through it is I. Another circular coil ‘B’ has a radius 2R and if 2I is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e. $B_A$ to $B_B$):

1. 4 : 1                             

2. 2 : 1

3. 3 : 1                             

4. 1 : 1

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 $4\mathrm{\pi }\times {10}^{-7}\mathrm{s}$

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{NI}}{\mathrm{b}}$                                  2. $\frac{2{\mathrm{\mu }}_0\mathrm{NI}}{\mathrm{a}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{NI}}{2(\mathrm{b}-\mathrm{a})}\ln \frac{\mathrm{b}}{\mathrm{a}}$                         4. $\frac{{\mathrm{\mu }}_0{\mathrm{I}}^{\mathrm{N}}}{2(\mathrm{b}-\mathrm{a})}\ln \frac{\mathrm{b}}{\mathrm{a}}$

The magnetic induction at the centre O in the figure shown is:                                                   

 1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right)$                                   2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left(\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}\right)$                                                         

 3. $\frac{{\mathrm{\mu }}_0\mathrm{i} }{4}\left({\mathrm{R}}_1-{}_{}{}^{}\mathrm{R}_2\right)$                                      4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4}\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)$       

A very long straight wire carries a current I. At the instant when a charge $+\underset{~}{O}$ at point P has velocity $\overrightarrow{v}$ , as shown, the force on the charge is:

1. Opposite to OX                            2. Along OX

3. Opposite to OY                             4. Along OY

A wire carrying a current i is placed in a uniform magnetic field in the form of the curve $y=\alpha \sin \left(\frac{\mathrm{\pi x}}{L}\right), 0\le x\le 2L$. The force acting on the wire is:

1. $\frac{iBL}{\mathrm{\pi }}$                                        2. $iBL\mathrm{\pi }$

3. $2iBL$                                        4. Zero

A wire in the form of a square of side ‘a’ carries a current i. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = ${\mathrm{\mu }}_0$)

1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{\pi a}}$                   2.  $\frac{{\mathrm{\mu }}_0\mathrm{i}\sqrt{2}}{\mathrm{\pi a}}$

3.  $\frac{2\sqrt{2} {\mathrm{\mu }}_0\mathrm{i}}{\mathrm{\pi a}}$             4.  $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\sqrt{2}\mathrm{\pi a}}$

A ring of radius R, made of an insulating material carries a charge Q uniformly distributed on it. If the ring rotates about the axis passing through its center and normal to the plane of the ring with constant angular speed $\omega$, then the magnitude of the magnetic moment of the ring is:

1. $Q\omega R^2$                       2. $\frac{1}{2}Q\omega R^2$

3. $Q{\omega }^{2}R$                       4. $\frac{1}{2}Q{\omega }^{2}R$

A straight section PQ of a circuit lies along the X-axis from x=$\frac{-\mathrm{a}}{2}$ to x= $\frac{\mathrm{a}}{2}$ and carries a steady current i. The magnetic field due to the section PQ at a point X = + a will be:

1. Proportional to a             2. Proportional to $a^2$
3. Proportional to $\frac{1}{a}$           4. Zero