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

step 1 We know that when two spherical conductors are connected by a conducting wire, then charge will

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

Two spherical conductors $A$ and $B$ of radii $1 \mathrm{~mm}$ and $\mathrm{mm}$ are separated by a distance of $5 \mathrm{~cm}$ and are uniformly charged. If the spheres are connected by 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) $1: 4$

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Key Concepts

Equipotentiality of Connected Conductors

When conductors are connected by a conductive wire, they share charge until they reach an identical electric potential. This equilibrium condition ensures that the potential difference between them is zero, which for spheres implies that the quantity Q/r (where Q is the charge and r is the radius of the sphere) is the same for both, leading to a proportional distribution of charge relative to their radii.

Electric Potential of a Charged Sphere

The electric potential on the surface of a charged spherical conductor is given by V = Q/(4???r), where Q is the total charge and r is the radius. This formula is key for understanding how connected spheres, having equal potential, end up with charges that differ in proportion to their radii.

Surface Electric Field of a Sphere

The magnitude of the electric field at the surface of a spherical conductor is given by E = Q/(4???r²). This relation shows that for spheres with differing radii but the same potential, the ratio of their surface electric fields is determined by the inverse ratio of their radii. Thus, even though the potential is equal, the electric fields can differ, illustrating the geometric effect on the field strength.

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