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
${u_0}\left[ {\frac{{\sqrt {39} }}{{10}}\hat i + \frac{3}{5}\hat j + \frac{1}{2}\hat k} \right]$
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Given below are two statements
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Given below are two statements
Statement $I$ : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle
Statement $II$ : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below
- [JEE MAIN 2022]
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.
Answer the following questions:
$(a)$ A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?
$(b)$ A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?
$(c)$ An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.