Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres

Two charged spherical conductors of radius `"R"_1` and `"R"_2` are connected by a wire.

(1) `\frac{R_1^2}{R_2^2}`
(2) `\frac{R_1}{R_2}`
(3) `\frac{R_2}{R_1}`
(4) ` \sqrt{(\frac{R_1}{R_2})}`

Option 3 is the Correct answer.

Explanation:

`"R"_1` = `"R"_2`

`"V"_1` = `"V"_2`

The potential will be equal as they are connected with wire.

= `\frac{"kq"_1}{"q"_2} = \frac{"kq"_2}{"q"_1}`

= `\frac{"q"_1}{"q"_2} = \frac{"R"_1}{"R"_2}`

= `\frac{\sigma_1}{\sigma_2} ` = `\frac{\frac{"q"_1}{4\pi "R"_1^2}}{\frac{"q"_2}{4\pi "R"_2^2}}`

= `\frac{"q"_1}{"q"_2} =( \frac{"R"_2}{"R"_1})^2`

= `\frac{\sigma_1}{\sigma_2} ` = `\frac{"R"_2}{"R"_1}`


Hence the Correct option is (B) `\frac{"R"_2}{"R"_1}`