At $t$ = $0$, a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o $ from the $x-$axis as shown in the figure. A constant magnetic field ${\vec B_0} = {B_0}\hat j$ is present in space. After a time interval $t_0$ velocity of particle may be:-
At $t$ = $0$, a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o $ from the $x-$axis as shown in the figure. A constant magnetic field ${\vec B_0} = {B_0}\hat j$ is present in space. After a time interval $t_0$ velocity of particle may be:-
- A
${u_0}\left[ {\frac{{\sqrt {39} }}{2}\hat i + \frac{3}{5}\hat j - \frac{{\hat k}}{{\sqrt 3 }}} \right]$
- B
${u_0}\left[ {\frac{{\hat i}}{{\sqrt 3 }} + \frac{{\hat j}}{{\sqrt 2 }} + \frac{{\hat k}}{{\sqrt 6 }}} \right]$
- C
${u_0}\left[ {\frac{{\sqrt {39} }}{{10}}\hat i + \frac{3}{5}\hat j + \frac{1}{4}\hat k} \right]$
- D
${u_0}\left[ {\frac{{\sqrt {39} }}{{10}}\hat i + \frac{3}{5}\hat j + \frac{1}{2}\hat k} \right]$
Similar Questions
A beam of protons with speed $4 \times 10^{5}\, ms ^{-1}$ enters a uniform magnetic field of $0.3\, T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to....$cm$
(Mass of the proton $=1.67 \times 10^{-27}\, kg$, charge of the proton $=1.69 \times 10^{-19}\,C$)
A beam of protons with speed $4 \times 10^{5}\, ms ^{-1}$ enters a uniform magnetic field of $0.3\, T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to....$cm$
(Mass of the proton $=1.67 \times 10^{-27}\, kg$, charge of the proton $=1.69 \times 10^{-19}\,C$)
- [JEE MAIN 2020]
A charged particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to
A charged particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to
Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_{\alpha}$ Which one of the following relation is correct?
Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_{\alpha}$ Which one of the following relation is correct?
- [AIEEE 2012]
A uniform electric field and a uniform magnetic field are produced, pointed in the same direction. An electron is projected with its velocity pointing in the same direction
A uniform electric field and a uniform magnetic field are produced, pointed in the same direction. An electron is projected with its velocity pointing in the same direction
- [AIEEE 2005]
A particle with ${10^{ - 11}}\,coulomb$ of charge and ${10^{ - 7}}\,kg$ mass is moving with a velocity of ${10^8}\,m/s$ along the $y$-axis. A uniform static magnetic field $B = 0.5\,Tesla$ is acting along the $x$-direction. The force on the particle is
A particle with ${10^{ - 11}}\,coulomb$ of charge and ${10^{ - 7}}\,kg$ mass is moving with a velocity of ${10^8}\,m/s$ along the $y$-axis. A uniform static magnetic field $B = 0.5\,Tesla$ is acting along the $x$-direction. The force on the particle is