(B) The radius of a circular path for a charged particle in a magnetic field is given by $R = \frac{mv}{qB}$.Since the particle is accelerated through

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$\left(\frac{R_1}{R_2}\right)^2$

(B) The radius of a circular path for a charged particle in a magnetic field is given by $R = \frac{mv}{qB}$.Since the particle is accelerated through a potential difference $V$,its kinetic energy is $KE = qV = \frac{1}{2}mv^2$,which implies $v = \sqrt{\frac{2qV}{m}}$.Substituting $v$ into the radius formula: $R = \frac{m}{qB} \sqrt{\frac{2qV}{m}} = \frac{\sqrt{2mqV}}{qB} = \frac{1}{B} \sqrt{\frac{2mV}{q}}$.Since $q$,$V$,and $B$ are constant for both particles,we have $R \propto \sqrt{m}$,which implies $m \propto R^2$.Therefore,the ratio of the masses is $\frac{m_X}{m_Y} = \left(\frac{R_1}{R_2}\right)^2$.

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

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Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter,they enter normally into a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is:

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A
$\left(\frac{R_2}{R_1}\right)^2$
B
$\left(\frac{R_1}{R_2}\right)^2$
C
$\frac{R_1}{R_2}$
D
$\frac{R_2}{R_1}$

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Moving Charges and Magnetism

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Motion of Charged Particle In Magnetic Field

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$A$ particle having a charge of $10\,\mu C$ and $1\,\mu g$ mass moves along a circular path of $10\, cm$ radius in the presence of a uniform magnetic field of $0.1\, T$. When the charge is at point $P$,a uniform electric field is applied in the region such that the charge moves tangentially with a constant speed. The value of the electric field is......$V/m$

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The magnetic force acting on a charged particle of charge $2\,\mu C$ in a magnetic field of $2\, T$ acting in the $y-$ direction,when the particle velocity is $(2\hat{i} + 3\hat{j}) \times 10^6\, m/s$ is:

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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..........

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Two ions of masses $4 \, amu$ and $16 \, amu$ have charges $+2e$ and $+3e$ respectively. These ions pass through a region of constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:

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An electron $(q = 1.6 \times 10^{-19}\, C)$ is moving at a right angle to a uniform magnetic field of $3.534 \times 10^{-5}\, T$. The time taken by the electron to complete one circular orbit is ...... $\mu s$.

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Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter,they enter normally into a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is:

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The magnetic force acting on a charged particle of charge $2\,\mu C$ in a magnetic field of $2\, T$ acting in the $y-$ direction,when the particle velocity is $(2\hat{i} + 3\hat{j}) \times 10^6\, m/s$ is:

$A$ 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..........

Two ions of masses $4 \, amu$ and $16 \, amu$ have charges $+2e$ and $+3e$ respectively. These ions pass through a region of constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:

An electron $(q = 1.6 \times 10^{-19}\, C)$ is moving at a right angle to a uniform magnetic field of $3.534 \times 10^{-5}\, T$. The time taken by the electron to complete one circular orbit is ...... $\mu s$.

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