First slide

Pontial due to

Question

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

Moderate

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

Solution

After redistribution, charges on them will be different, but they will acquire common potential i.e.,
$k \frac{Q_{1}}{r_{1}} = k \frac{Q_{2}}{r_{2}} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{r_{1}}{r_{2}} As σ = \frac{Q}{4 {πr}^{2}} \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{Q_{1}}{Q_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{r_{2}}{r_{1}} \Rightarrow σ \propto \frac{1}{r}$
i.e., surface charge density on smaller sphere will be more.

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