(C) In the velocity selector,the electric force and magnetic force on the ion must balance for it to pass through undeflected:$qE = qvB$$v = \frac{E}{

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(C) In the velocity selector,the electric force and magnetic force on the ion must balance for it to pass through undeflected:$qE = qvB$$v = \frac{E}{B}$In the deflection chamber,the magnetic force provides the centripetal force for the circular motion of the ion:$qvB = \frac{mv^2}{r}$$r = \frac{mv}{qB}$Substituting the value of $v = \frac{E}{B}$ and using $q = e$ for a singly charged ion:$r = \frac{m(E/B)}{eB} = \frac{mE}{eB^2}$

Class 12 Physics Moving Charges and Magnetism Motion of Charged Particle In Magnetic Field

Medium

Consider the mass spectrometer as shown in the figure. The electric field between the plates is $E \ V/m$,and the magnetic field in both the velocity selector and in the deflection chamber has magnitude $B$. Find the radius $r$ for a singly charged ion of mass $m$ in the deflection chamber.

A
$\frac{mE}{eB}$
B
$\frac{mE^2}{eB}$
C
$\frac{mE}{eB^2}$
D
$\frac{mE}{Be^2}$

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Moving Charges and Magnetism

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Motion of Charged Particle In Magnetic Field

$A$ proton is projected with a speed of $2 \times 10^6 \ m/s$ at an angle of $60^{\circ}$ to the $x$-axis. If a uniform magnetic field of $0.104 \ T$ is applied along the $y$-axis,the path of the proton is:

Medium

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$A$ singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\,keV$ and is projected perpendicularly into a magnetic field $B$ of magnitude $0.5\,T$. The radius of the path formed will be . . . . . . $cm$.

MediumJEE MAIN 2022

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An electron experiences a force $\vec{F} = (4.0\,\hat{i} + 3.0\,\hat{j}) \times 10^{-13}\,N$ in a uniform magnetic field when its velocity is $\vec{v}_1 = 2.5\,\hat{k} \times 10^7\,m/s$. When the velocity is redirected to $\vec{v}_2 = (1.5\,\hat{i} - 2.0\,\hat{j}) \times 10^7\,m/s$,the magnetic force on the electron is zero. The magnetic field $\vec{B}$ is:

Medium

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$A$ proton, a deuteron, and an $\alpha$-particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speeds are in the ratio of..........

DifficultJEE MAIN 2021

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$A$ particle of mass $m$ and charge $q$ has an initial velocity $\vec{v} = v_{0} \hat{j}$. If an electric field $\vec{E} = E_{0} \hat{i}$ and a magnetic field $\vec{B} = B_{0} \hat{i}$ act on the particle,its speed will double after a time:

MediumJEE MAIN 2020

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Consider the mass spectrometer as shown in the figure. The electric field between the plates is $E \ V/m$,and the magnetic field in both the velocity selector and in the deflection chamber has magnitude $B$. Find the radius $r$ for a singly charged ion of mass $m$ in the deflection chamber.

Similar Questions

$A$ proton is projected with a speed of $2 \times 10^6 \ m/s$ at an angle of $60^{\circ}$ to the $x$-axis. If a uniform magnetic field of $0.104 \ T$ is applied along the $y$-axis,the path of the proton is:

$A$ singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\,keV$ and is projected perpendicularly into a magnetic field $B$ of magnitude $0.5\,T$. The radius of the path formed will be . . . . . . $cm$.

$A$ proton, a deuteron, and an $\alpha$-particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speeds are in the ratio of..........

$A$ particle of mass $m$ and charge $q$ has an initial velocity $\vec{v} = v_{0} \hat{j}$. If an electric field $\vec{E} = E_{0} \hat{i}$ and a magnetic field $\vec{B} = B_{0} \hat{i}$ act on the particle,its speed will double after a time:

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