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

step 1 It is given that two spherical conductors A and B are connected. So A and B two spherical conduc

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 surface of spheres $A$ and $B$ is (A) $1: 4$ (B) $4: 1$ (C) $1: 2$ (D) $2: 1$

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Key Concepts

Spherical Conductors

Spherical conductors are typically analyzed using the principles of electrostatics where the electric field at a point on the surface is determined by the charge distribution and geometry. The fundamental relationships used are E = Q/(4???R²) for the electric field and V = Q/(4???R) for the potential, with Q being the charge and R the radius of the conductor.

Electrostatic Equilibrium

When conductors are connected by a conducting wire, they reach electrostatic equilibrium, meaning that they attain the same electric potential. This equipotential condition forces the charges to redistribute between the conductors so that V_A = V_B, regardless of the individual sizes or radii, and is key to solving problems involving charge sharing.

Relationship Between Surface Electric Field and Conductor Radius

Under the equipotential condition, while the potential is the same on both conductors, the surface electric field, given by E = V/R, is inversely proportional to the radius of the conductor. This inverse relationship implies that a smaller conductor will have a greater surface electric field compared to a larger one when both are at the same potential.

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