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Pontial due to

Question

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density $σ$ . They are brought in contact and separated. What will be the new surface charge densities on them?

Moderate

A

$σ_{1} = \frac{5}{6} σ, σ_{2} = \frac{5}{2} σ$
B

$σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{6} σ$
C

$σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{3} σ$
D

$σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$

Solution

when spheres are kept in contact, charge redistribution takes place to get same potential.
Total combined charge = $20 {πR}^{2} σ$ .
Potential of both the spheres become equal, hence Q = $\frac{Q^{I}}{2}$ where Q is the charge on sphere of radius R and $Q^{I}$ is the charge on sphere of radius 2R.
Thus charge on sphere of radius R becomes $\frac{20 {πR}^{2} σ}{3}$ , while charge on sphere of radius 2R becomes $\frac{40 {πR}^{2} σ}{3}$
Hence new charge densities will be
$σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$

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