A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to
A particle of charge $q$ and mass $m$ moving with a velocity $v$ along the $x$-axis enters the region $x > 0$ with uniform magnetic field $B$ along the $\hat k$ direction. The particle will penetrate in this region in the $x$-direction upto a distance $d$ equal to
- A
Zero
- B
$\frac{{mv}}{{qB}}$
- C
$\frac{{2mv}}{{qB}}$
- D
Infinity
Similar Questions
A particle of mass $M$ and charge $Q$ moving with velocity $\mathop v\limits^ \to $ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is
A particle of mass $M$ and charge $Q$ moving with velocity $\mathop v\limits^ \to $ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is
- [AIEEE 2003]
A particle of mass $0.6\, g$ and having charge of $25\, nC$ is moving horizontally with a uniform velocity ${\rm{1}}{\rm{.2}} \times {\rm{1}}{{\rm{0}}^{\rm{4}}}\,m{s^{ - 1}}$ in a uniform magnetic field, then the value of the magnetic induction is $(g = 10\,m{s^{ - 2}})$
A particle of mass $0.6\, g$ and having charge of $25\, nC$ is moving horizontally with a uniform velocity ${\rm{1}}{\rm{.2}} \times {\rm{1}}{{\rm{0}}^{\rm{4}}}\,m{s^{ - 1}}$ in a uniform magnetic field, then the value of the magnetic induction is $(g = 10\,m{s^{ - 2}})$
An electron moving with a velocity ${\vec V_1} = 2\,\hat i\,\, m/s$ at a point in a magnetic field experiences a force ${\vec F_1} = - 2\hat j\,N$ . If the electron is moving with a velocity ${\vec V_2} = 2\,\hat j \,\,m/s$ at the same point, it experiences a force ${\vec F_2} = + 2\,\hat i\,N$ . The force the electron would experience if it were moving with a velocity ${\vec V_3} = 2\hat k$ $m/s$ at the same point is
An electron moving with a velocity ${\vec V_1} = 2\,\hat i\,\, m/s$ at a point in a magnetic field experiences a force ${\vec F_1} = - 2\hat j\,N$ . If the electron is moving with a velocity ${\vec V_2} = 2\,\hat j \,\,m/s$ at the same point, it experiences a force ${\vec F_2} = + 2\,\hat i\,N$ . The force the electron would experience if it were moving with a velocity ${\vec V_3} = 2\hat k$ $m/s$ at the same point is
A charged particle of charge $\mathrm{e}$ and mass $\mathrm{m}$ is moving in an electric field ${{\rm{\vec E}}}$ and magnetic field ${{\rm{\vec B}}}$ Construct dimensionless quantities and quantities of dimension [T]-1
A charged particle of charge $\mathrm{e}$ and mass $\mathrm{m}$ is moving in an electric field ${{\rm{\vec E}}}$ and magnetic field ${{\rm{\vec B}}}$ Construct dimensionless quantities and quantities of dimension [T]-1
A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} kg$, charge of the electron $=1.6 \times 10^{-19} C$.]
Which of the following option($s$) is(are) correct?
$(A)$ The value of $x$ for $H^{+}$ion is $4 cm$.
$(B)$ The value of $x$ for an ion with $A_M=144$ is $48 cm$.
$(C)$ For detecting ions with $1 \leq A_M \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 cm$.
$(D)$ The minimum width $w$ of the region of the magnetic field for detecting ions with $A_M=196$ is $56 cm$.
A positive, singly ionized atom of mass number $A_M$ is accelerated from rest by the voltage $192 V$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} kg$, charge of the electron $=1.6 \times 10^{-19} C$.]
Which of the following option($s$) is(are) correct?
$(A)$ The value of $x$ for $H^{+}$ion is $4 cm$.
$(B)$ The value of $x$ for an ion with $A_M=144$ is $48 cm$.
$(C)$ For detecting ions with $1 \leq A_M \leq 196$, the minimum height $\left(x_1-x_0\right)$ of the detector is $55 cm$.
$(D)$ The minimum width $w$ of the region of the magnetic field for detecting ions with $A_M=196$ is $56 cm$.
- [IIT 2024]