Q 12-02-122JEE MainJEE Main 2022 (26 Jul, Shift 2)Easy
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 surfaces of spheres $A$ and $B$ will be
Answer: (B) $2 : 1$
Connected spheres reach the same potential: $\dfrac{kq_A}{r_A} = \dfrac{kq_B}{r_B}$. Then $E = \dfrac{kq}{r^2} = \dfrac Vr\propto\dfrac1r$:
$$\frac{E_A}{E_B} = \frac{r_B}{r_A} = \frac{10}{5} = 2$$
Solution by Sreeraj P, M.Sc Physics