Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle -

(1) depends on v and not on R

(2) depends on R and not on v

(3) is independent of both v and R

(4) depends on both v and R

The magnetic force acting on a charged particle of charge $-2\mu C$ in a magnetic field of 2T acting in y-direction, when the particle velocity is $\left(2\hat{i}+3\hat{j}\right)\times {10}^6<mspace\; width="1em"></mspace>m{s}^{-1}$ is.

(a) 8 N in -z-direction

(b) 4 N in z-direction

(c) 8 N in y-direction

(d) 8 N in z-direction

A closed-loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RO are $F_1,<mspace\; width="1em"></mspace>F_2<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>F_3$ respectively and are in the plane of the paper and along with the directions shown the force on the segment QP is 

(a)$F_3+F_1-F_2$

(b)$\sqrt{{\left(F_3-F_1\right)}^2+F_2^2}$

(c)$\sqrt{{\left(F_3-F_1\right)}^2-F_2^2}$

(d)$F_3-F_1+F_2$

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

 A narrow electron beam passes undeviated through an electric field E = $3\times {10}^4<mspace\; width="1em"></mspace>\mathrm{volt}/\mathrm{m}$ and an overlapping magnetic field $\mathrm{B}=2\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{Weber}/{\mathrm{m}}^2$. If electric field and magnetic field are mutually perpendicular. The speed of the electrons is 
1. 60 m/s                          2. $10.3\times {10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$
3. $1.5\times {10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$                4. $0.67\times {10}^{-7<mspace\; width="1em"></mspace>}\mathrm{m}/\mathrm{s}$

A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength $20<mspace\; width="1em"></mspace>{\mathrm{Vm}}^{-1}$ and 0.5 T at right angles to the direction of motion of the electrons. What is the velocity of the electrons

1. 20 ${\mathrm{ms}}^{-1}$                  2. 40 ${\mathrm{ms}}^{-1}$ 
3. 8 ${\mathrm{ms}}^{-1}$                    4. 5.5 ${\mathrm{ms}}^{-1}$

Order of q/m ratio of proton, $\alpha$-particle and electron is

(a) $\mathrm{e}>\mathrm{p}>\mathrm{\alpha }$               (b) $\mathrm{p}>\mathrm{\alpha }>\mathrm{e}$

(c) $\mathrm{e}>\mathrm{\alpha }>\mathrm{p}$               (d) None of these

${\mathrm{O}}^{++},<mspace\; width="1em"></mspace>{\mathrm{C}}^{+},<mspace\; width="1em"></mspace>{\mathrm{He}}^{++}$ and ${\mathrm{H}}^{+}$ ions are projected on the photographic plate with the same velocity in a mass spectrograph. Which one will strike the farthest?

1. ${\mathrm{O}}^{++}$                  2. ${\mathrm{C}}^{+}$
3. ${\mathrm{He}}^{++}$                4. ${\mathrm{H}}_2^{+}$

A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85$\mu A$and subjected to the magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is:

1. $4.55<mspace\; width="1em"></mspace>\mu J$

2. $2.3<mspace\; width="1em"></mspace>\mu J$

3. $1.15<mspace\; width="1em"></mspace>\mu J$

4. $9.8<mspace\; width="1em"></mspace>\mu J$