A particle of charge $q$ and mass $m$ moving with a velocity $v$ along $x -$ 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 up to a distance $d$ equal to

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Answer 1

Lorentz force $F = q (v \times B) = q (v \hat{i} \times B \hat{k}) = - q v B \hat{j}$
The particle move in a circle, the plane of the circle is perpendicular to the direction of magnetic field.
Centripetal force is provided by the Lorentz force.
$q v B = \frac{m v ^{2}}{r}$
$\Rightarrow r = \frac{m v}{q B}$

Answer 2

Lorentz force

F = q (v \times B) = q (v \hat{i} \times B \hat{k}) = - q v B \hat{j}

The particle move in a circle, the plane of the circle is perpendicular to the direction of magnetic field.
Centripetal force is provided by the Lorentz force.

q v B = \frac{m v ^{2}}{r}

\Rightarrow r = \frac{m v}{q B}

A particle of charge $q$ and mass $m$ moving with a velocity $v$ along $x -$ 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 up to a distance $d$ equal to

$Z e r o$

$\frac{m v}{q B}$

$\frac{2 m v}{q B}$

$I n f i n i t y$

A positive charge ' $q$ ' of mass ' $m$ ' is moving along the +x axis. We wish to apply a uniform magnetic field $B$ for time $Δ t$ , so that the charge reverses its direction, crossing the y axis at a distance $d$ . Then:

A charged particle of charge $+ q$ , mass $m$ is moving with initial velocity ' $v$ ' as shown in figure in a uniform magnetic field $B (- k)$ . Select the correct alternative / alternatives :

Revise with Concepts

Motion in the Presence of Magnetic Field

Motion in the Presence of Magnetic Field - Problems L1

A particle of charge q and mass m moving with a velocity v along x−axis enters the region x>0 with uniform magnetic field B along the k^ direction. The particle will penetrate in this region in the x−direction up to a distance d equal to

Zero

qBmv​

qB2mv​

Infinity

Lorentz force F=q(v×B)=q(vi^×Bk^)=−qvBj^​ The particle move in a circle, the plane of the circle is perpendicular to the direction of magnetic field. Centripetal force is provided by the Lorentz force. qvB=rmv2​ ⇒r=qBmv​

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A charged particle of charge +q, mass m is moving with initial velocity 'v' as shown in figure in a uniform magnetic field B(−k). Select the correct alternative / alternatives :

Revise with Concepts

Motion in the Presence of Magnetic Field

Motion in the Presence of Magnetic Field - Problems L1

A particle of charge $q$ and mass $m$ moving with a velocity $v$ along $x -$ 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 up to a distance $d$ equal to

$Z e r o$

$\frac{m v}{q B}$

$\frac{2 m v}{q B}$

$I n f i n i t y$

A positive charge ' $q$ ' of mass ' $m$ ' is moving along the +x axis. We wish to apply a uniform magnetic field $B$ for time $Δ t$ , so that the charge reverses its direction, crossing the y axis at a distance $d$ . Then:

A charged particle of charge $+ q$ , mass $m$ is moving with initial velocity ' $v$ ' as shown in figure in a uniform magnetic field $B (- k)$ . Select the correct alternative / alternatives :