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

What is the result of an electric charge in uniform motion?

Two particles each of mass \(m\) and charge \(q\) are attached to the two ends of a light rigid rod of length \(2R\). The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. What is the ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod?
1. \(\frac{q}{2m}\)
2. \(\frac{q}{m}\)
3. \(\frac{2q}{m}\)
4. \(\frac{q}{\pi m}\)

Current i is carried in a wire of length L. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field B will be:

1. $\frac{Li{B}^2}{2}$                     2. $\frac{L{i}^{2}B}{2}$

3. $\frac{L^{2}iB}{4\mathrm{\pi }}$                     4. $\frac{L{i}^{2}B}{4\mathrm{\pi }}$

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an $\mathrm{\alpha }$-particle to describe a circle of the same radius in the same field?

1. 2 MeV                  2. 1 MeV

3. 0.5 MeV               4. 4 MeV

Two straight long conductors AOB and COD are perpendicular to each other and carry currents ${\mathrm{i}}_1$ and ${\mathrm{i}}_2$ . The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ACBD is: 

1. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi a}}({\mathrm{i}}_1+{\mathrm{i}}_2)$                    2. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi a}}({\mathrm{i}}_1-{\mathrm{i}}_2)$

3. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi a}}{\left({\mathrm{i}}_1^2+{\mathrm{i}}_2^2\right)}^{1/2}$                4. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi a}}\frac{{\mathrm{i}}_1{\mathrm{i}}_2}{({\mathrm{i}}_1+{\mathrm{i}}_2)}$

A particle mass m, charge Q, and kinetic energy T enter a transverse uniform magnetic field of induction $\overrightarrow{B}$. After 3sec the kinetic energy of the particle will be : 

1. 3T

2. 2T

3. T

4. 4T

An electron of mass m and charge q is traveling with a speed v along a circular path of radius r at right angles to a uniform of the magnetic field B. If the speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of:

1. $\frac{r}{4}$                           

2. $\frac{r}{2}$ 

3. $2r$                           

4. $4r$