Two uniformly charged spherical conductors A and B of radii 5 mm and… | JEE Main 2022 (26 Jul, Shift 2)

Q73JEE Main 2022 · 26 JUL · SHIFT 2Medium

Electric Potential & Equipotentials

Two uniformly charged spherical conductors $A$ and $B$ of radii $5\text{ mm}$ and $10\text{ mm}$ are separated by a distance of $2\text{ cm}$ . 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:

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Answer: (b)

Connected spheres are at equal potential, so $E = \frac{V}{r} \propto \frac{1}{r}$ (separation is large compared with radii).
$\frac{E_A}{E_B} = \frac{r_B}{r_A} = \frac{10}{5} = 2$
So the answer is (b) $2 : 1$ .

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