(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

Medium

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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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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$A$ proton, a deuteron (nucleus of ${ }_1 H^2$) and an $\alpha$-particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is:

$A$ charge $Q$ is moving through a distance $d\vec{l}$ in a magnetic field $\vec{B}$. Find the value of the work done by the magnetic field.

$A$ 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 a 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:

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