(C) When the spheres are connected by a conducting wire,charge flows until their potentials become equal,i.e.,$V_A = V_B$.Since $V = \frac{kQ}{r}$,we

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(C) When the spheres are connected by a conducting wire,charge flows until their potentials become equal,i.e.,$V_A = V_B$.Since $V = \frac{kQ}{r}$,we have $\frac{kQ_A}{r_A} = \frac{kQ_B}{r_B}$,which implies $\frac{Q_A}{Q_B} = \frac{r_A}{r_B}$.The electric field at the surface of a spherical conductor is given by $E = \frac{kQ}{r^2}$.Therefore,the ratio of the electric fields is $\frac{E_A}{E_B} = \frac{kQ_A / r_A^2}{kQ_B / r_B^2} = \frac{Q_A}{Q_B} \times \left( \frac{r_B}{r_A} \right)^2$.Substituting $\frac{Q_A}{Q_B} = \frac{r_A}{r_B}$,we get $\frac{E_A}{E_B} = \frac{r_A}{r_B} \times \frac{r_B^2}{r_A^2} = \frac{r_B}{r_A}$.Given $r_A = 1\, mm$ and $r_B = 2\, mm$,the ratio is $\frac{E_A}{E_B} = \frac{2\, mm}{1\, mm} = 2 : 1$.

Class 12 Physics Electric Potential and Capacitance Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

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Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are placed at a distance of $5\, cm$ from each other. They carry equal charges. If the spheres are connected by a conducting wire,they reach an equilibrium state. The ratio of the magnitudes of the electric fields at the surfaces of spheres $A$ and $B$ is ........

A
$4 : 1$
B
$1 : 2$
C
$2 : 1$
D
$1 : 4$

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Electric Potential and Capacitance

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Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

$A$ dipole consisting of two charges $\pm q$ separated by a distance $2a$ is placed with its centre at a distance $D$ from the center of a grounded conducting sphere of radius $R$ $(D \gg a)$. When the dipole moment vector is perpendicular to the line joining the two centres (those of the dipole and sphere),the total charge induced on the sphere is:

MediumKVPY 2021

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$A$ point charge $Q$ is placed inside a cavity within a solid isolated conducting sphere. Consider points $A$, $B$ and $C$, where the magnitudes of the electric fields are $E_A$, $E_B$ and $E_C$, respectively. Point $A$ is inside the material of the conductor. Points $B$ and $C$ are at the same distance from the center of the solid sphere. The correct option is:

MediumNEET 2026

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$A$ point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0)$. An isolated uncharged spherical conductor is fixed with its center at $(4, 0, 0)$. The potential and the induced electric field at the center of the sphere are:

DifficultJEE MAIN 2013

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Given below are two statements.
Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements,choose the most appropriate answer from the options given below.

MediumJEE MAIN 2022

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Two metal spheres $A$ and $B$ of radii $a$ and $b$ $(a < b)$ respectively are at a large distance apart. Each sphere carries a charge of $100 \mu C$. The spheres are connected by a conducting wire,then

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$A$ point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0)$. An isolated uncharged spherical conductor is fixed with its center at $(4, 0, 0)$. The potential and the induced electric field at the center of the sphere are:

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