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 ${\mathrm{ms}}^{-1}$

In Bainbridge mass spectrograph a potential difference of 1000 V is applied between two plates distant 1 cm apart and magnetic field in B = 1T. The velocity of undeflected positive ions in m/s from the velocity selector is

(1)${10}^7<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$                    

(2) ${10}^4<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$

(3) ${10}^5<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$                   

(4) ${10}^2<mspace\; width="1em"></mspace>\mathrm{m}/\mathrm{s}$ 

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. H⁺

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 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 

1.${\mathrm{<mspace\; width="1em"></mspace>F}}_3+F_1-F_2$

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

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

4. $F_3-F_1+F_2$

A galvanometer having a coil resistance of $60\Omega$ shows full scale deflection when a current of 1.0A passes through it. It can be converted into an ammeter to read currents upto 5.0A by 

1. putting in series resistance of 240$\Omega$

2. putting in parallel resistance of 240$\Omega$

3. putting in series resistance of 15$\Omega$

4. putting in parallel resistance of 15$\Omega$

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.

1. 8 N in -z-direction

2. 4 N in z-direction

3. 8 N in y-direction

4. 4 N in y-direction