(B) The work done by the electric field on a charge $q$ accelerated through a potential difference $V$ is equal to its kinetic energy.$W = qV = \frac{

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(B) The work done by the electric field on a charge $q$ accelerated through a potential difference $V$ is equal to its kinetic energy.$W = qV = \frac{1}{2}mv^2$Since the mass $m$ and potential difference $V$ are the same for both particles,we have $v^2 \propto q$,which implies $v \propto \sqrt{q}$.Therefore,the ratio of their speeds is:$\frac{v_A}{v_B} = \sqrt{\frac{q_A}{q_B}} = \sqrt{\frac{q}{9q}} = \sqrt{\frac{1}{9}} = \frac{1}{3}$.Thus,the ratio of their speeds is $1 : 3$.

Class 12 Physics Electric Potential and Capacitance Electric potential

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$A$ particle $A$ has a charge of $+q$ and a particle $B$ has a charge of $+9q$. Both particles have the same mass $m$. If both particles are released from rest through the same potential difference,the ratio of their speeds will be .......

A
$1 : 2$
B
$1 : 3$
C
$1 : 2\sqrt{2}$
D
None of these

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Electric Potential and Capacitance

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Electric potential

Two concentric hollow spherical conductors of radii $R$ and $2R$ have charges $Q$ and $-Q$ respectively. Find the electric potential at a distance of $\frac{3R}{2}$ from the centre. $\left[K=\frac{1}{4\pi\varepsilon_0}\right]$

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An electron with an initial speed of $4.0 \times 10^6 \, m/s$ is brought to rest by an electric field. The mass and charge of an electron are $9 \times 10^{-31} \, kg$ and $1.6 \times 10^{-19} \, C$, respectively. Identify the correct statement.

MediumKVPY 2013

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$A$ charge $Q$ is distributed over three concentric spherical shells of radii $a, b, c$ $(a < b < c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre,where $r < a$,would be

DifficultJEE MAIN 2019

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$A$ spherical drop of liquid carrying charge $Q$ has potential $V_0$ at its surface. If two drops of same charge and radius combine to form a single spherical drop,then the potential at the surface of the new drop is (Assume $V=0$ at infinity.)

MediumTS EAMCET 2019

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$A$ proton has a mass $1.67 \times 10^{-27} \,kg$ and charge $+1.6 \times 10^{-19} \,C$. If the proton is accelerated through a potential difference of $1$ million volts,then the kinetic energy is ......... $J$.

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$A$ particle $A$ has a charge of $+q$ and a particle $B$ has a charge of $+9q$. Both particles have the same mass $m$. If both particles are released from rest through the same potential difference,the ratio of their speeds will be .......

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Two concentric hollow spherical conductors of radii $R$ and $2R$ have charges $Q$ and $-Q$ respectively. Find the electric potential at a distance of $\frac{3R}{2}$ from the centre. $\left[K=\frac{1}{4\pi\varepsilon_0}\right]$

An electron with an initial speed of $4.0 \times 10^6 \, m/s$ is brought to rest by an electric field. The mass and charge of an electron are $9 \times 10^{-31} \, kg$ and $1.6 \times 10^{-19} \, C$, respectively. Identify the correct statement.

$A$ charge $Q$ is distributed over three concentric spherical shells of radii $a, b, c$ $(a < b < c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre,where $r < a$,would be

$A$ spherical drop of liquid carrying charge $Q$ has potential $V_0$ at its surface. If two drops of same charge and radius combine to form a single spherical drop,then the potential at the surface of the new drop is (Assume $V=0$ at infinity.)

$A$ proton has a mass $1.67 \times 10^{-27} \,kg$ and charge $+1.6 \times 10^{-19} \,C$. If the proton is accelerated through a potential difference of $1$ million volts,then the kinetic energy is ......... $J$.

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