Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distan

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2. Electric Potential and Capacitance

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Two uniformly charged spherical conductors $A$ and $B$ of radii $5 mm$ and $10 mm$ are separated by a distance of $2 cm$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $A$ and $B$ will be .

A

$1:2$

B

$2:1$

C

$1:1$

D

$1:4$

(JEE MAIN-2022)

Solution

$V _{ A }= V _{ B }$

$\frac{ KQ _{ A }}{ R _{ A }}=\frac{ KQ _{ B }}{ R _{ B }}$

$\frac{ Q _{ A }}{ Q _{ B }}=\frac{ R _{ A }}{ R _{ B }}=\frac{1}{2}$

$E _{ A }=\frac{ KQ _{ A }}{ R _{ A }^{2}} ; E _{ B }=\frac{ KQ _{ B }}{ R _{ B }^{2}}$

$\frac{ E _{ A }}{ E _{ B }}=\frac{ Q _{ A }}{ Q _{ B }} \times \frac{ R _{ B }{ }^{2}}{ R _{ A }{ }^{2}}=\frac{ R _{ B }}{ R _{ A }}=\frac{2}{1}$

Standard 12

Physics

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(AIIMS-1999)