Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively

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Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10 C are connected by a copper wire and then they are separated. Then

Options:

A . Both the spheres will have the same charge of 10 C

B . Surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere

C . Surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere

D . Surface charge density on the two spheres will be equal

Answer: Option C
:
C
After redistribution, charges on them will be different, but they will acquire common potential
i.e.

k \frac{Q_{1}}{r_{1}} = k \frac{Q_{2}}{r_{2}} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{r_{1}}{r_{2}}

As

σ = \frac{Q}{4 π r^{2}} \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} \Rightarrow σ \propto \frac{1}{r}

i.e. surface charge density on smaller sphere will be more.

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