(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

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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.

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

The region between $y = 0$ and $y = d$ contains a magnetic field $\vec B = B\hat k$. $A$ 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

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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.

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The region between $y = 0$ and $y = d$ contains a magnetic field $\vec B = B\hat k$. $A$ 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

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