Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm a

step 1 For this question here R1 divided by R2 is equal to 1mm divided by 2mm is equals to 1 by 2 and w

Two spherical conductors A and B of radii 1 mm and 2 mm...

Two spherical conductors $A$ and $B$ of radii $1 \mathrm{~mm}$ and $2 \mathrm{~mm}$ are separated by a distance of $5 \mathrm{~cm}$ and are uniformly charged. 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 $A$ and $B$ is (a) $4: 1$ (b) $1: 2$ (c) $2: 1$ (d) $1: 4$

Key Concepts

Electrostatic Equilibrium

In electrostatic equilibrium, charges in a conductor are distributed so that the electric field inside the conductor is zero. This means when two conductors are connected by a conducting wire, the charges will flow between them until they reach the same potential, ensuring no net movement of charge and achieving equilibrium.

Equipotential Condition in Connected Conductors

When conductors are connected by a wire, they become equipotential. This implies that despite differences in their geometric sizes, the electric potential (voltage) on each conductor becomes equal. This concept is crucial for determining how charge distributes between objects of different sizes, as the potential on a charged sphere is inversely proportional to its radius.

Electric Field on a Conductor's Surface

The electric field just outside a charged conductor is perpendicular to its surface and is directly related to the surface charge density. For a spherical conductor, this field can be expressed by the formula E = Q/(4???R²), where Q is the charge and R is the radius of the sphere. This illustrates how the curvature of the surface influences the field strength.

Relationship Between Charge, Potential, and Radius

The potential on the surface of a spherical conductor is given by V = Q/(4???R). When two spheres are in contact and share the same potential, the charge on each must adjust in proportion to their radii. This relationship between charge, potential, and radius is essential for understanding how the electric fields on the surfaces of connected spheres compare.

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