Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ 1 and 2, respectively. The ratio 
is
Text Solution
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When two conducting spheres are in contact, they achieve the same electric potential.
Consider two metal spheres with radii R and 3R that have the same surface charge density 
.
For a conductive sphere, the potential V of a sphere can be expressed as 
, where r is the radius of the sphere and 
is the permittivity of free space.
When the two spheres are brought into contact and then separated, they equalize their potentials:
Thus, the equations become:
Substituting for the radii:
From this, we can solve for the ratio of the surface charge densities:
Therefore, the ratio of the surface charge densities on the smaller sphere to the larger sphere after contact is 3.
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