Two uniformaly charged spherical conductors A and B having radius 1 mm and 2 mm are separated

step 1 Hi friends here it is given two spheres of radius r a and r b are uniformly charged r a having t

Two uniformaly charged spherical conductors A and B having...

Two uniformaly charged spherical conductors $\mathrm{A}$ and $\mathrm{B}$ having radius $1 \mathrm{~mm}$ and $2 \mathrm{~mm}$ are separated by a distance of $5 \mathrm{~cm} .$ If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $\mathrm{A}$ and $\mathrm{B}$ is..... (A) $4: 1$ (B) $1: 2$ (C) $2: 1$ (D) $1: 4$

Key Concepts

Surface Electric Field of a Sphere

The magnitude of the electric field just outside the surface of a conducting sphere can be expressed as E = kQ/R^2. This formula shows that the surface electric field is inversely proportional to the square of the radius, implying that for a given potential (and thus linked charge via Q = VR/k), larger spheres will have a smaller electric field at their surfaces compared to smaller spheres.

Charge Distribution in Connected Conductors

Connecting conductors with a wire forces them to share charge in such a way that the final charge distribution results in equal electric potential. However, charges do not distribute equally by magnitude; rather, the distribution is influenced by the geometrical properties (such as radii) of the conductors. This leads to differing surface electric fields despite the uniformity of potential.

Electrostatic Equilibrium

When conductors are connected by a wire, they reach a state of electrostatic equilibrium, meaning that the electric potential is uniform across all connected conductors. This key concept ensures that even if the conductors have different shapes or sizes, their surfaces will adjust charge distributions until all points on them are at the same potential, thereby eliminating any driving force for charge movement.

Electric Potential of a Conducting Sphere

The electric potential on the surface of a charged conducting sphere is determined by the formula V = kQ/R, where k is Coulomb’s constant, Q is the charge, and R is the radius of the sphere. This relationship indicates that for spheres at the same potential, the amount of charge on each sphere is directly proportional to its radius.

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