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Two charged metallic spheres of radii r(...

Two charged metallic spheres of radii `r_(1)` and `r_(2)` are touched and separated . Calculate the ratio of their
(1) Charges
(2) Potential
(3) Self energy
(4) Electric field at the surface
(5) Surface charge density

A

Charges

B

Potential

C

Self energy

D

Electric field at the surface `" "` (v) Surface charge density

Text Solution

Verified by Experts

After touching potential will be same
so `V_(1)=V_(2)`
`K(Q_(1))/(r_(1))=K(Q_(2))/(r_(2))` then
(i) `(Q_(1))/(Q_(2))=(r_(1))/(r_(2))`
(ii) `(V_(1))/(V_(2))=1 " " or " " V_(1): V_(2)=1:1`
(iii) `because U (1)/(2)CV^(2) "so" ,U prop C " ""or " U prop r `
`implies (U_(1))/(U_(2))=(r_(1))/(r_(2))`
(iv) `because E = (V)/(d) " " "so" , " " E prop (1)/(d) "then" (E_(1))/(E_(2))=(r_(2))/(r_(1))`
(v) `because V = (sigma r)/(epsilon_(0))`
`implies ` At same potential `sigma`r = constant
`implies (sigma_(1))/(sigma_(2))=(r_(2))/(r_(1))`
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