Home
Class 12
PHYSICS
Two chareged sperical conductors of radi...

Two chareged sperical conductors of radill `R_(1) and R_(2)` when connected by a connecting wire acquire charges `q_(1) and q_(2)` respectively. Find the ratio of their charge densities in terms of their radil ?

Text Solution

Verified by Experts

Two spherical conductors, when connected by a wire will share charges till, they common potential. Thus,
`(q_(1))/(4pi in_(0) R_(1)) = (q_(2))/(4pi in_(0) R_(2)) or (q_(1))/(q_(2)) = (R_(1))/(R_(2))`
Ratio of surface density of charges is
`(sigma_(1))/(sigma_(2)) = (q_(1)//4pi in_(0) R_(1)^(2))/(q_(2)//4pi in_(0) R_(2)^(2)) = (q_(1))/(q_(2)) xx (R_(2)^(2))/(R_(1)^(2)) = (R_(1))/(R_(2)) xx (R_(2)^(2))/(R_(1)^(2)) = (R_(2))/(R_(1))`
Promotional Banner

Similar Questions

Explore conceptually related problems

(a) Derive the expression for the capacitance of a parallel plate capacitor having plate area A and plate separation d. (b) Two charged spherical conductors of radii R_(1) and R_(2) when connected by a conducting wire acquire charges q_(1) and q_(2) respectively. Find the ratio of their surface charge densities in terms of their radii.

Two charged spherical conductors of radius R_1 and R_2 are connected by a wire. Then the ratio of surface charge densities of the spheres (sigma_1)/(sigma_2) is

Two metallic s pheres of radii R_(1) and R_(2) are connected b y a thin wire. If +q_(1)~ and +q_(2) are the charges on the two s pheres then

Two concentric spherical shells of radius R_(1) and R_(2) (R_(2) gt R_(1)) are having uniformly distributed charges Q_(1) and Q_(2) respectively. Find out total energy of the system.

Find force acting between two shells of radius R_(1) and R_(2) which have uniformly distributed charges Q_(1) and Q_(2) respectively and distance between their centres is r.

Two conducting spheres of radii r_(1) and r_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

The insulated spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

Two concentric uniformly charge spherical shells of radius R_(1) and R_(2) (R_(2) gt R_(1)) have total charges Q_(1) and Q_(2) respectively. Derive an expression of electric field as a function of r for following positions. (i) r lt R_(1) (ii) R_(1) le r lt R_(2) (iii) r ge R_(2)