The region between $y = 0$ and $y = d$ contains a magnetic field $\vec B = B\hat z$ A particle of mass $m$ and charge $q$ enters the region with a velocity $\vec v = v\hat i$. If $d = \frac{{mv}}{{2qB}}$ , the acceleration of the charged particle at the point of its emergence at the other side is
The region between $y = 0$ and $y = d$ contains a magnetic field $\vec B = B\hat z$ A particle of mass $m$ and charge $q$ enters the region with a velocity $\vec v = v\hat i$. If $d = \frac{{mv}}{{2qB}}$ , the acceleration of the charged particle at the point of its emergence at the other side is
- [JEE MAIN 2019]
- A
$\frac{{qvB}}{m}\,\left( {\,\frac{{ \hat j + \hat i}}{{\sqrt 2 }}} \right)$
- B
$\frac{{qvB}}{m}{\mkern 1mu} \left( {{\mkern 1mu} \frac{{\sqrt 3 }}{2}{\mkern 1mu} \hat i + \frac{1}{2}\hat j} \right)$
- C
$\frac{{qvB}}{m}\,\left( {\,\frac{{ - \hat j + \hat i}}{{\sqrt 2 }}} \right)$
- D
$\frac{{qvB}}{m}{\mkern 1mu} \left( {\frac{1}{2}\hat j - \frac{{\sqrt 3 }}{2}\hat i} \right)$
Similar Questions
A uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3 R}{2}$ (region $2$ in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along $x$-axis enters region $2$ from region $1$ at point $P_1(y=-R)$. Which of the following option(s) is/are correct?
$[A$ For $B>\frac{2}{3} \frac{p}{QR}$, the particle will re-enter region $1$
$[B]$ For $B=\frac{8}{13} \frac{\mathrm{p}}{QR}$, the particle will enter region $3$ through the point $P_2$ on $\mathrm{x}$-axis
$[C]$ When the particle re-enters region 1 through the longest possible path in region $2$ , the magnitude of the change in its linear momentum between point $P_1$ and the farthest point from $y$-axis is $p / \sqrt{2}$
$[D]$ For a fixed $B$, particles of same charge $Q$ and same velocity $v$, the distance between the point $P_1$ and the point of re-entry into region $1$ is inversely proportional to the mass of the particle
A uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3 R}{2}$ (region $2$ in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along $x$-axis enters region $2$ from region $1$ at point $P_1(y=-R)$. Which of the following option(s) is/are correct?
$[A$ For $B>\frac{2}{3} \frac{p}{QR}$, the particle will re-enter region $1$
$[B]$ For $B=\frac{8}{13} \frac{\mathrm{p}}{QR}$, the particle will enter region $3$ through the point $P_2$ on $\mathrm{x}$-axis
$[C]$ When the particle re-enters region 1 through the longest possible path in region $2$ , the magnitude of the change in its linear momentum between point $P_1$ and the farthest point from $y$-axis is $p / \sqrt{2}$
$[D]$ For a fixed $B$, particles of same charge $Q$ and same velocity $v$, the distance between the point $P_1$ and the point of re-entry into region $1$ is inversely proportional to the mass of the particle
- [IIT 2017]
A charged particle moves in a magnetic field $\vec B = 10\,\hat i$ with initial velocity $\vec u = 5\hat i + 4\hat j$ The path of the particle will be
A charged particle moves in a magnetic field $\vec B = 10\,\hat i$ with initial velocity $\vec u = 5\hat i + 4\hat j$ The path of the particle will be
A particle of specific charge (charge/mass) $\alpha$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and magnetic field $\vec B = {B_0}\hat k$. Its velocity at $(x_0 , y_0 , 0)$ is ($(4\hat i + 3\hat j)$ . The value of $x_0$ is:
A particle of specific charge (charge/mass) $\alpha$ starts moving from the origin under the action of an electric field $\vec E = {E_0}\hat i$ and magnetic field $\vec B = {B_0}\hat k$. Its velocity at $(x_0 , y_0 , 0)$ is ($(4\hat i + 3\hat j)$ . The value of $x_0$ is:
An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6}\, ms ^{-1}$. It enters a region of uniform electric field of $300 \,V / cm$ pointing along $+ y$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $x$ direction will be
An electron is moving along $+x$ direction with a velocity of $6 \times 10^{6}\, ms ^{-1}$. It enters a region of uniform electric field of $300 \,V / cm$ pointing along $+ y$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $x$ direction will be
- [JEE MAIN 2020]
A particle of mass $m$ and charge $q$, accelerated by a potential difference $V$ enters a region of a uniform transverse magnetic field $B$. If $d$ is the thickness of the region of $B$, the angle $\theta$ through which the particle deviates from the initial direction on leaving the region is given by
A particle of mass $m$ and charge $q$, accelerated by a potential difference $V$ enters a region of a uniform transverse magnetic field $B$. If $d$ is the thickness of the region of $B$, the angle $\theta$ through which the particle deviates from the initial direction on leaving the region is given by